His 86-year-old body was somewhat frail, and his voice at time a little shaky. But the words were as forceful as ever yesterday as veteran black educator Benjamin E. Mays urged the 1981 graduating class of the University of the District of Columbia not to use past sufferings as an excuse for failure, but rather to work harder than those "who had no such handicaps to overcome."

In a rousing speech interrupted frequently by applause, Mays said, "We are now required to complete in the open market with those who have been more favorably circumstanced than we are for several centuries. Our inadequancies will be printed in the press . . . Nobody will explain the reason for our shortcomings . . .

"There is only one thing we can do, what Negroes have always done: make brick without straw, lift ourselves by our bootstraps when we have no boots. . . The only thing left for a poor man to do to overcome his poverty is to find a good job, work hard and save."

Mays' address was delivered before 1,000 graduates and hundreds of other spectors under a bright morning sun in the outdoor plaza of UDC's Van Ness campus, and marked the last commencement over which outgoing university president Lisle C. Carter Jr. will officiate.

Mays' speech yesterday was markedly different from that given at last year's commencement, when Mayor Marion Barry called on the university's predominantly black graduating class not to criticize other blacks -- especially those in power like himself, who are grappling with longstanding prolbems.

Mays', the former president of Morehouse College in Atlanta, and former dean of the Howard University School of Religion, gave an upbeat, sermon-like speech, invoking the names of such black success stories as educator Mary McLeod Bethune, historian W. E. B. DuBois, former cabinet secretary Patricia Harris and songstress Marian Anderson, and encouraged the graduates not only to achieve in life, but to strive to overachieve.

"Whether we like it or not, we must read more and socialize less, study more and frolic less, do more research . . . write books and become recognized in our fields. It is better by far for you graduates to be known by the books you publish, than by the house you live in," said Mays, the author of eight books.

Mays was speaking at UDC at the same time Vice President George Bush was addressing the graduates of Howard University on the Reagan administration's commitment to civil rights and the poor. The silver-haired educator threw one brief but sharply worded barb at the Reagan administration. e

"The present administration here in the nation's capital seems to have little concern for the man farthest down," Mays said. "It is sheer hypocrisy to expound brotherhood and foster caste, to preach Christian fellowship, then deny it to certain groups because they are Africans or Negroes."

Mays, who has served as president of Atlanta's school board for the past 12 years, also asked the graduates to examine "to what end" they have sought education. Too often, he said, education becomes mixed up with the pursuit of status.

I know people who display their ego by buying homes larger and more costly than they need, and costing more than what is necessary. I do not condemn them for this. But I do condemn them if they do this to put themselves above the poor and so-called 'common man.'"

Mays' speech struck a personal note with graduate Gary Andre Cooper, a D.C. policeman who received his bachelor's degree in business management yesterday.

"I asked myself, 'Hey, why do I want a Cadillac?' And I found I wanted it just for status. But once you obtain these [material] things, what good do they do you?" asked Cooper, who was holding his red-covered diploma tightly in his hands. It took him eight years of study to get it, he said.

Roxcella Janet Brown of Landover, who recieved a bachelor of science degree in technical vocational education, said she agreed with Mays that blacks "have to recognize what's happened to them in the past, recognize what's hampered them from being the first to get the job, look at these things, evaluate them and go from there."

For Mildred McKinney of Northeast Washington, who received a bachelor's degree in public administration, yesterday's exercises and Mays' address marked the end of more than a decade of studies. "It was the most beautiful speech I've heard," she said, "in my past 12 years in school."