The state’s voter identification law, which took effect in June 2013, is one of the most stringent of its kind in the country. It requires voters who show up at the polls to identify themselves with one of five forms of government-issued ID, including a driver’s license, a passport or a concealed-handgun license. Every form of acceptable identification includes a photograph of the voter. Several other states with voter ID laws, including Georgia and Indiana, have looser rules, including allowing expired driver’s licenses.

Those in Texas lacking one of the five types of identification must obtain a so-called election identification certificate, a card similar to a driver’s license that is issued by the state Department of Public Safety. Although election ID cards are free, prospective voters have to pay fees to obtain certain documents to verify their identity, such as a certified copy of a birth certificate.

The fees associated with election ID cards, and the traveling that prospective voters must undertake to obtain them, led the federal court in Washington to strike down the law in 2012. The three-judge panel found that would-be voters without a valid ID would need to apply for an election ID card at a Department of Public Safety office, but many of Texas’ 254 counties lacked one.

Lawyers suing the state said that blacks and Hispanics disproportionately lacked one of the five forms of approved ID compared with white Texans, and that the process of obtaining an election ID card imposed burdens on minority voters, many of whom are poor and lack access to transportation. Men and women who claim that the law has prevented them from voting will testify at the trial.

One of those who may testify is Imani Clark, 22, a college student who used to vote in Waller County using her student ID but has not voted since the law took effect. She does not have one of the approved forms of identification and has been unable to travel to a state office to apply for an election ID.

“She doesn’t have access to a car,” said Natasha M. Korgaonkar, a lawyer for the NAACP Legal Defense and Educational Fund who is representing Ms. Clark. “Waller County is rural Texas. There’s no public transportation available to her.”