A young South African man convicted of murdering his wealthy parents and brother and maiming his sister in a frenzied axe attack was handed three life sentences on Thursday.

Judge Siraj Desai described 23-year-old Henri Van Breda's January 2015 rampage as "savage and vicious" with "an almost unprecedented degree of disregard for one's family".

"Each murderous attack on a family member is a severe crime and warrants the severest punishment," Mr Desai told the packed Western Cape High Court in Cape Town after the headline-making trial.

Van Breda, who wore a light grey suit, blue shirt and patterned tie, was also jailed for 15 years for the attempted murder of his sister.

After a trial that had sought in vain to understand the motive for the bloodbath, Van Breda remained emotionless as the sentence was handed down.

He was then led away by court officers as his girlfriend watched from the public gallery.

He had denied murdering his 21-year-old brother Rudi and parents Martin, 54, and Teresa, 55, and leaving his sister Marli struggling with near-fatal injuries to her head, neck and throat after the bloody attack.