The number of blacks in the Army has increased by more than 50 percent since the draft ended in 1972, but racial problems seem to be under control, according to the Army's latest assessment of the trends.

The prospect is for the Army to become progressively blacker because a rising percentage of blacks are signing up and opting to reenlist, figures in the new, 63-page assessment indicate.

Army leaders have expressed no concern that the proportion of young blacks in the Army is running ahead of that in the general population, although Army Secretary Clifford L. Alexander Jr. worries that their higher reenlistment rates may indicate perceived or actual discrimination in the civilian job market.

In a letter accompanying the Army's assessment of how well it did in providing equal opportunity in 1976 and 1977, Alexander and Gen. Bernard W. Rogers, Army chief of staff, said "significant progress" had been made but "much remains to be accomplished."

In the report, the Army said "major areas of concern" on the racial front are "the disproportionate number" of dishonorable and bad-conduct discharges given to blacks, "racial imbalances" within job specialities, and a shortage of black officers in National Guard and reserve units.

"In general," said the report, both black and white officers surveyed "do not perceive race problems to be a major unit personnel problem."

In surveying the enlisted ranks, the Army found that some soldiers believed race relations in their units had worsed from 1976 to 1977 but that "the majority of all soldiers felt that the racial situation had remained about the same."

Pentagon figures show that in 1972, the last year for draft calls, 15.6 percent of the Army was black. As of Sept. 30, 1977, that figure had climbed to 23.9 percent, a 53 percent increase.

Breaking down the figures between officers and enlisted people, the percentage of black officers rose from 3.9 percent to 6.1 percent between 1972 and 1977, while the proportion of black enlisted climbed from 17.5 to 26.4 percent.

Back in 1972, blacks comprised 15.3 percent of the volunteers signing up for Army duty. In fiscal 1977, that percentage had nearly doubled to 29.4 percent.

The recently released Army report attributed this upsurge partly to the "dramatic increase" in the proportion of blacks graduating from high school and thus qualifying for Army service. (The percentage of blacks graduating from high school jumped from 27.5 percent in 1967 to 42.2 percent in 1975.)

Another explanation for the increase in black enlistments, said the Army, is the higher employment rate among blacks, 37.5 percent in 1977 compared to 13.5 percent for whites.