The Federal Housing Adminstration, faced with an unprecedented demand for its loan guarantees and the lower interest rates they bring, has fallen victim to a paperwork crunch that can delay applications as long as two months.

FHA applications began climbing rapidly at the end of the summer as the agency's maximum interest rate started to decline. According to the Department of Housing and Urban Development, applications totaled 28,084 in August, 44,906 in September, 51,841 in October and a record 82,545 last month, when the FHA interest rate dropped to 12 percent.

HUD's Washington field office alone received 3,640 applications in November, by far the largest number of any area in the country. That number was a 527 percent increase over November 1981.

And, according to lenders, the tide has not crested. "The FHA hasn't seen the worst of it yet," said Dr. Mark J. Riedy, executive vice president of the Mortgage Bankers Association of America. "The phenomenon caught everyone by surprise" and mortgage bankers themselves "are undergoing internal delay. . . . Wait till we get done digesting it."

HUD Secretary Samuel R. Pierce Jr. this week called the surge "good news" because of what it represents about the nation's housing market. He termed it a "good indication that the president's economic recovery program is taking hold and the housing industry is on the road to recovery."

But for the individual loan seeker, delay can be very awkward. At a minimum, the borrower, if he is buying a house, must wait longer to get into his new home, or, if he is refinancing, must continue his higher payments for another month or more.

A more acute problem is the element of uncertainty that the delay introduces. With rates changing as rapidly as they have been, neither lender nor borrower can be sure when the application is made what the terms of the loan will be by the time settlement is reached.

Conversation with Washington-area lenders indicated that processing of FHA-guaranteed loans can take anywhere from seven to 10 weeks, whereas a conventional loan, for which the borrower can expect to pay one to two percentage points more, can be processed in under a month.

One area lender said that a month ago, when FHA's rate was 12 1/2 percent, he was quoting applicants that figure plus one point. (A point is a fee equal to 1 percent of the loan.)

But now, this lender said, the FHA rate has dropped to 12 percent, so "we cannot legally close at" 12 1/2 percent. The difference, he said, will be made up in points, though he declined to specify how many.

If the economic picture changes and interest rates turn up, a different problem can arise. At settlement the lender will want the new, higher rate.

"We close at the maximum allowable rate," said one lender, which can mean "a substantial difference" in the payments. Sometimes this difference is enough to disqualify the buyer.

"This happens from time to time," said another lender, who added it was fairly frequent during the rapid runup of rates last year.

Pierce said this week that HUD is aware of the problem and is working to solve it. "I assure you we are taking whatever steps are available to us to minimize delay," he said. "We are doing everything we possibly can."

He said HUD is hiring more people and shifting people in the department and among field offices "to try to get the job done."

He added that HUD is also working on a plan to move more of the processing work "to the private sector." Under this plan, called "delegated processing," mortgage bankers would be authorized to do more of the paperwork, such as credit checks, now done by FHA field offices.

HUD officials also said the agency is making greater use of "fee people" -- appraisers and loan evaluators, for example, who work for a fee -- to try to speed things up.

The mortgage bankers' Riedy said that members of the lending industry have been meeting with HUD officials to work out details for delegated processing. He said he expects such a plan to be in effect by mid-March and for it to have a very beneficial effect.

"We'll gear up with permanent or temporary staff . . . and get the time way down," he said.

He said he feels the early spring implementation is important because after that more rate changes are to be expected. "We are now in a period of relative rate stability . . . . In a more volatile environment, this sort of delay would be disastrous."