WARNING: This story contains graphic details that may be distressing to some readers.

The man accused of murdering Grace Millane went on a Tinder date with another woman while the backpacker's body was contorted in a suitcase in his apartment, court hears.

Photo: Supplied / Facebook

The 27-year-old, who has name suppression, is on trial in the High Court at Auckland this month accused of murdering Ms Millane.

The British backpacker's body was found buried in the Waitākere Ranges a week after she disappeared in Auckland's CBD on the eve of her 22nd birthday.

Her family, who are at court today, raised the alarm after she didn't respond to birthday messages.

This morning the court heard the accused met her for a date in Auckland's CBD after the pair matched on the dating app Tinder.

Crown prosecutor Robin McCoubrey said CCTV cameras filmed them kissing and enjoying the night at a burger bar, Mexican cafe and finally a bar.

"They were plainly comfortable in one another's company that evening," he said.

"Both parties probably anticipated sexual activity and at some point around 9.40pm that evening on 1 December the two entered [the defendant's] apartment at CityLife."

The court heard the accused initially told police he'd met Ms Millane for a drink before parting ways with her on Victoria Street but then changed his story.

The man later said he and Ms Millane went back to his apartment where she initiated rough sex, before they took intimate photographs of each other, the court heard.

Mr McCoubrey said the man told police the rough sex continued and he then fell asleep in the shower before going to bed to sleep.

He told police Ms Millane was dead and bleeding from her nose when he woke up the following morning, the prosecutor said.

Mr McCoubrey said it might be expected that the man would panic or call 111 for help but he instead Google searched 'Waitākere Ranges' and 'hottest fire' in the early hours of that morning.

"It's plain that Ms Millane is dead at that point. What [the defendant] is doing here is trying to find a place to hide her body in the Waitākeres, where she did end up buried, and is trying to find a means of disposing of her body by fire," Mr McCoubrey said.

The court heard the man then watched pornography on a website at 1.41am. Between 1.46am and 1.49am he took seven explicit photographs of Ms Millane's body.

"To be perfectly clear on this, the Crown says she is dead at this point," Mr McCoubrey said.

The court heard the man also photographed her leg and foot before watching more pornography.

Mr McCoubrey said the defendant hired a car and purchased a large suitcase before contorting Ms Millane's body into the bag.

That morning he also text messaged another woman to confirm a date he'd earlier arranged on Tinder, the court heard.

Mr McCoubrey said the pair met for a few drinks in Ponsonby later that afternoon, where he calmly talked about a person who got done for manslaughter after having rough sex that went wrong.

"He doesn't seem concerned by the presence of a dead body in his apartment but goes up the road to have a date with another woman at a bar," the prosecutor said.

"You may think he's testing out a version of events he may later have to rely on to see how it sounds."

The court heard the man later returned to his apartment, wheeled Ms Millane's body in the suitcase to his hire car on a baggage carrier and then drove it to the Waitākere Ranges where he buried it.

Mr McCoubrey said a pathologist would tell the jury that the cause of her death was pressure to the neck, and the expert would also explain a number of bruises consistent with restraint in Ms Millane's upper chest area and inner upper arms.

Mr McCoubrey said it was the Crown's case that the man had strangled Ms Millane and that he was guilty of murder.

"Only two people can tell us what happened in that room. One of them can't tell us and the other one hasn't told us the truth about what happened."

Death was 'unforeseen and unintended' - defence lawyer

The defendant cried as his defence lawyer Ian Brookie made a brief opening address this morning.

Mr Brookie told the jury the backpacker's death occured as an "unforeseen and unintended consequence" of a "perfectly ordinary" consensual casual sexual encounter between two young people.

"What sets this night apart is that Ms Millane died as a result of what they consensually engaged in during their time together ... and she died as a result."

Mr Brookie said his client had restricted Ms Millane's breathing by applying pressure to her neck.

"That act was done with her knowledge, encouragement and only with the goal of sexual pleasure in mind," he said.

"Ms Millane is not to blame but because the Crown says that [the accused] is to blame and criminal to the extent that they say he murdered her, we need to show you why he is not."

"Put simply, this death was an accident. He certainly didn't murder her. Neither of them expected this act would cause her death."

He told the jury they may not like what his client did after the young woman died but they could draw little value from his actions in determining what he was thinking when he put his hands around her throat that night.

The lawyer for the accused said Ms Millane's death was an accident.

Justice Moore reminded the jury they are absolutely prohibited from making their own enquiries about the case online or on social media. He said the jury must rely only on evidence presented in court and must not make their minds up until they had heard all the evidence.

Grace Millane's parents David and Gillian Millane have flown to New Zealand for the trial.

They sat in the front row of the court's public gallery this morning with victim support, a family liaison officer and the lead detective in the police investigation, Scott Beard.

Evidence from Ms Millane's father, David, was read to the court by Mr McCoubrey.

Mr Millane said his daughter had just graduated from university and intended to be away for a year.

He said she had been in regular contact with her family, and had bought clothes and toys for her niece and sent them back home.

Mr Millane said his daughter was very close to her mother.

However, Mr Millane said she had never discussed online dating with her parents - but he wouldn't have expected her to.

Mrs Millane cried as her husband's evidence was read to the court.

More than 20 journalists were in court to report on the proceedings, including international media.

The Crown's case is led by Crown Solicitor for Auckland Brian Dickey, with Robin McCoubrey and Litia Tuiburelevu.

It is up to the Crown to prove the murder charge; the defendant does not have to prove his innocence.

The prosecution must prove the charge beyond a reasonable doubt, which means the jury must be sure he is guilty to convict him.

The 27-year-old defendant is represented by Auckland lawyers Ian Brookie, Ron Mansfield and Claire Farquhar.

The Crown will call 36 witnesses, including police officers who worked on the case, experts and Ms Millane's father David Millane.

The trial before Justice Moore and a jury of seven women and five men is set down for a month.