A verbal duel between two Pentagon weapons specialists, one who warns that costs are running out of control and the other who insists they are not, will take place before the Senate Budget Committee as soon as their seconds can work out the final details.

On one side is Franklin (Chuck) Spinney, 37, an analyst in the Pentagon's Program Analysis and Evaluation shop. The former Air Force captain and aeronautical engineer conducted a detailed study of past cost overruns, concluded that the vaunted "learning curve" that is supposed to bring down the cost of weapons is pretty much of a myth and warned that if history is allowed to repeat itself, President Reagan's program to rearm America will run out of money long before it is completed.

PA&E, as the program analysis office is called, is supposed to act as the manure separator for the defense secretary and his top civilian deputies. Analysts like Spinney are paid to pierce the shiny brochures of defense contractors and the slide shows of the military services in assessing weaponry. The findings of PA&E, and the systems analysis shop that preceded it, often have infuriated generals, admirals and their allies in Congress. But defense secretaries traditionally have been grateful for this independent viewpoint.

This time, however, Secretary Caspar W. Weinberger is acting more furious than grateful for Spinney's findings. In a particularly harsh review of his own analyst's work, David S.C. Chu, director of PA&E, said: "This was a historical study . . . . It does not address the future . . . . There isn't a study to release. There's a set of people's scribblings and other conversations which have been scarfed up by somebody and stapled together and given out . . . . There isn't something we can give out that would help illuminate the issue."

"Horsefeathers!" and worse, replied Spinney fans in the Pentagon and Congress. Spinney, they say, has put together an impressive, two-hour briefing that throws bright light on the implications of Reagan's weapon-buying spree.

Sen. Charles E. Grassley (R-Iowa) heard about the study, visited Spinney at the Pentagon and came away a convert who is demanding that the Pentagon release the study and allow Spinney to testify before the Senate Budget Committee.

"Spinney has, in his own quiet way, dropped a bomb," Grassley wrote the Senate Republican Conference last week. Congress has no choice but to diagnose Spinney's study and the defense budget and prescribe an appropriate remedy."

Sen. Nancy Landon Kassebaum (R-Kan.) said she, too, has heard about the Spinney study and its assertion that weapon costs have been underestimated by as much as 1,000 percent. "It's clear to me that the Defense Department is suppressing this information that could be immensely helpful to use in the budget process."

Grassley, Kassebaum and a third Republican on the committee, Slade Gorton (Wash.), have written Chairman Pete V. Domenici (R-N.M.) formally requesting that Spinney, George Kuhn, the author of a critical report on Pentagon procurement for the Heritage Foundation, and Martin A. Margolis, deputy director of the PA&E office, who reviewed the Spinney findings, all appear as witnesses.

"If true," the senators wrote, "underfunding could present a major problem to the Pentagon, the administration and Congress."

The committee originally planned to call Richard D. DeLauer, undersecretary of defense for research and engineering, to rebut Spinney's findings.

DeLauer, a former aerospace executive, considers the Spinney report a flimsy piece of work that fails to give credit to the procurement control exerted by the new team at the Pentagon, with the tight cost lid that was clamped on the B1 bomber as his exhibit A.

Although still willing to testify if requested, DeLauer is more inclined to let Spinney and his boss, Chu, fight it out before the Senate committee.

Whether DeLauer testifies or not, a study he commissioned last year could prove troublesome as the Pentagon tries to shoot down Spinney's study.

The DeLauer report, presented in secret to top Pentagon executives on Jan. 7, 1982, warned that it might cost as much as $750 billion more than the Reagan administration has budgeted for fiscal 1984 through 1988 to buy all the weapons the Joint Chiefs of Staff said they would need to carry out the president's program to rearm America.

One of DeLauer's slides from that secret briefing sounded like the warning trumpets of Spinney, Kuhn and others getting so much attention these days: "The matrix shows that the fiscal year 1984-88 gap could be as large as $750 billion," it said. "My best guess is that the fiscal year 1984-88 gap will be about $300 billion, 20 percent of the FYDP five-year defense plan ."