The Reagan administration's effort to prosecute young men who don't register for the draft has produced few indictments or convictions, although the Justice Department says such efforts are "priority cases" and Attorney General William French Smith said more than a year ago that "there will certainly be hundreds" of indictments.

Of the 263,000 men who are more than a year late in registering, the government has indicted 15, convicted seven and sentenced two to jail terms, and no one is currently serving time for not registering.

Two indictments have been handed down so far this year, after a wave of 13 late last summer and fall, and no fresh wave seems to be in the offing. Moreover, in two of the cases brought to trial, judges have ruled either the registration statute or the prosecution procedures invalid. Although both those cases are on appeal, those rulings cast a shadow on future prosecutions.

At the end of this week, the Justice Department received from Selective Service a computer tape with the names of 70,000 probable non-registrants. Those names join more than 5,600 that Selective Service already had sent to Justice for investigation and possible prosecution.

Justice Department spokesman John Russell said of the fresh inundation of cases: "No, we're not going to be able to handle 70,000 names. We simply don't have the resources. We'll do the best we can."

Justice received a computer tape of 5,151 names Feb. 16, and shipped 93 cases to local attorneys on April 27. Those cases were chosen at random by a computer.

No further cases from that first tape have been referred for investigation, according to Russell, and he said he didn't know what the schedule for referring cases was, "or even if there is a schedule."

"There has been no directive to slow down any enforcement," Russell said. Some U.S. attorneys, however, have not moved on the cases sent to them for prosecution.

Every month for the last year, Greg Smucker of Elkhart, Ind., has been in touch with the U.S. attorney in South Bend. Smucker, a Mennonite, has not registered.

"Last June," Smucker said last week, "I was informed that I would probably be indicted in July. Each month since then, the U.S. attorney has pushed it off, saying he didn't have time, or it wasn't a pressing issue.

"It's been an emotional strain, for sure," said Smucker, who is one of three men from Elkhart in this position. "It's kind of a big thing to have hanging over your head."

Nearly 10.4 million men have registered for the draft since registration was resumed July 21, 1980, according to Joan Lamb of Selective Service. The overall compliance rate is 96.2 percent. In the group of men who would be drafted first, those aged 20 to 25, the compliance rate is 98.7 percent.

In all, 410,000 men have not registered for the draft.

Justice has received 5,626 cases for investigation from Selective Service since July 20, 1981, according to court documents. And, according to those same documents, Justice has referred 435 cases to U.S. attorneys for investigation and prosecution.

Lamb said that prosecution seems to be effective in getting men to register. Last summer and fall, with the ripple of indictments, the number of registrations jumped dramatically, from 120,000 a month to 150,000 a month.

Barry Lynn, the just-retired president of Draft Action, a national anti-draft group, said this week, "There is still no stomach on the part of U.S. attorneys to open the floodgates of prosecution. I cannot imagine that there will be."

Lynn says that local U.S. attorneys "are reluctant to bring the cases. They can't always win. And the sentences they are getting when they win are so modest as to make the whole effort appear to be a gross waste of judicial resources."

Two of the government's seven convictions involved jail sentences and are on appeal. Of the remaining five men, one was sentenced to time served, one to unsupervised probation and three to alternative service for up to two years. One man, brought to trial, registered. The remaining seven indictments are pending.

Since January, Selective Service has been working at the tedious task of identifying non-registrants and transmitting their names to Justice for prosecution. The point, despite the high compliance rate, is equity, according to Lamb: "The fellows who aren't registering are victimizing those who have." If a draft is instituted, she points out, those who have registered have a higher chance of being called because of those who have not.

But prosecuting non-registrants is more difficult than identifying them by cross-matching state driver's license lists with Selective Service records.

The men indicted so far had notified officials by letter of their refusal to register, and set up the government's cases. The cases going to Justice on computer tapes now are names, addresses and Social Security numbers. These require time-consuming investigation and evidence-building by FBI agents and local attorneys before indictments can be contemplated.