The number of federal and state prisoners is growing at the highest rate since the government began keeping statistics in 1926, according to a new study by the Justice Department.

The study, which covered the first six months of 1982, projected an annual increase of more than 14 percent in the number of prisoners -- at a time when prison systems are severely overcrowded and state and federal budgets strained.

The states most seriously affected, the study said, were Texas, California, New York and Florida. The four account for one-third of all state prisoners in the country; each has a prison population of more than 25,000.

The study attributed the rise in prison population to increased admissions and declining releases.

"Widespread adoption of new sentencing and parole laws has lengthened prison stays," it said. "Mandatory sentencing laws have been passed in most states. . . and parole has been abolished in four states." In addition, some states have passed tougher laws against drunken driving.

The study found that males between the ages of 20 and 29 continue to be the most likely to end up in prison. During the 1970s the number of prisoners in that group grew by more than 35 percent.

Although women make up only 4 percent of the prison population, their number is also rising dramatically. In the first half of 1982, the number of female prisoners increased by 11 percent. As of June 30, there were 17,142 women in state and federal prisons.

The report said that the number of female prisoners has doubled since 1974 while the number of male prisoners has increased by 70 percent.

Shortly after becoming attorney general, William French Smith appointed a task force on violent crime. It recommended that the government spend $2 billion to help the states build prisons, but the recommendation was never implemented, and federal budget cuts have strained state budgets even further.

According to a report this year by the American Civil Liberties Union, prison systems in 28 states, the District of Columbia, Puerto Rico and the Virgin Islands are under court orders to improve because they are violating constitutional rights of prisoners. In most of those systems, overcrowding is a factor.