Profits of Martin Marietta Corp. leaped more than 80 percent in the first quarter while Reynolds Metals Co. earnings of $38 million in the same period represented an improvement of some $50 million over a loss in the first quarter last year.

Moreover, officers of the two Fortune 500 companies said yesterday they expect business to remain robust for the rest of 1979, and both firms are planning major capital spending programs to expand output capacity.

Martin Marietta and Reynolds are two of the largest industrial corporations in the Middle Atlantic states, and both have extensive nationwide operations. Their reports yesterday provided additional evidence that the economy remains unusually strong despite forecasts of recession.

Bethesda-based Martin, a diversified aluminum, chemicals, aerospace and construction materials firm, reported that profits in the January-March quarter were a record $32.8 million ($1.29 a share) compared with $17.9 million (71 cents) in the same 1978 period.

Each of Martin's five major divisison produced improvements in quarterly results as sales advanced substantailly to $437 million from $348 million.

Reynolds, the nation's second-largest aluminum producer, reported first-quarter profits of $38.3 million ( $2 a share) compared with a year-earlier loss of $11 million as sales increased to $776 million from $608 million.

Speaking to stockholders at the annual meeting in Richmond' yesterday, Chairman David P. Reynolds also revelaed a doubling of capital expansion plans this year. Reynolds now expects to spend $250 million and will be operating its aluminum plants at 100 percent of capacity by late spring, the company officer stated.

"We are expecting a strong first half . . . and with many economists now pulling back from earlier predictions of an economic slowdown or recession in the latter half of the year, it appear that 1979 as a whole will be another very good year for our company." Reynolds told his stockholders.

Similarly, Martin Chairman J. Donald Rauth said he is optimistic that 1979 "will produce results even more attractive than those we achieved in 1978," which was a record year.

"The first quarter's results reflect continuing strong momentum in our aluminum, chemicals and aerospace companies . . . cement and aggregates [companies] enjoyed high levels of activity in March as winter weather moderated in most of their regional markets except the Upper Midwest and New England," Rauth added.

For Reynolds, the record first-quarter results reflect a positive swing in foreign currency translation and exchange losses (a loss of 33 cents a share in the recent quarter compared with a loss of $1.49 a share a year earlier), improved profit margins and a sharp jump in aluminum shipments, chairman Reynolds said.

But he said management remains unsatified by the company's rate of return on invested capital, which was 10.6 percent in the 12 months ended March 31. "For some years eernings and return were too low to provide for major expansion and upgrading of facilities . . . it is now imperative that we ungrade our facilities and plan for future expansion," he said.

With demand for aluminum up throughout the world, Reynolds is reactivating its only idle reduction plant in Corpus Christi, Tex., next month.

In other earnings statements, regional banking firms reported substantial first-quarter gains.

National Saving & Trust Co., of Washington posted a 25 percent increase in profits to $1 million ($2.32 a share) compared with $845, 000 ($1.85) a year earlier. Deposits rose to $429 million from $349 million and direction declaried a quarterly dividend of $1 a share, payable May 1 to owners of record April 20.

Bank of Virginia Co., at its annual million from $349 million, and direc-quarter operating profits of $3.7 million (79 cents a share) compared with $3.1 million (67 cents) last year.

First Maryland Bancorp, holding company for First National Bank of Maryland, reported a 38 percent increase in first-quarter operating profits to $4.5 million ($1.2o a share) from $3.1 million (87 cents).