Martin Marietta Corp. and Southern Railway Co., two of the largest business enterprises based in the Washington area, yesterday reported substantial increases in business volume and profitability in 1979 -- adding up to a banner year for each firm.

MCI Communications Corp., Union Trust Bancorp of Maryland and Flow General Inc. also reported gains, while American Realty Trust listed a net loss.

Martin Marietta, a nationwide aluminum, aerospace, chemicals and construction aggregates company based in Bethesda, said 1979 profits rose to $178 million ($7.10 a share) from $135 million ($5.54) as sales increased to $2.06 billion from $1.76 billion.

In the fourth quarter alone, earnings rose at a much more modest pace to $37.3 million ($1.50) from $36.6 million ($1.44) and sales increased to $569 million from $507 million. Earnings from operations before taxes actually declined in the recent three months to $52.7 million from $60 million, the company's statement revealed.

Each of the company's operating companies -- including cement -- achieved record sales and corporate profits during the year, Martin Marietta said.

Southern Railway, one of the two major rail systems in the southeastern states, said earnings last year inceased more than 26 percent to $160.6 million ($10.39 a share) from $127.3 million ($8.35) the previous year, as revenues rose 16 percent to $1.47 billion.

Chairman Stanley Crane said the record performance enabled the company's directors to approve an increase in the quarterly dividend rate yesterday of 12 cents a share to 92 cents -- the ninth payout boost in the last decade. The higher dividend will be paid March 15 to owners of record Feb. 15.

In the fourth quarter, Southern's profits rose to $33.3 million ($2.13) from $30.8 million ($2.00). Revenues were up 17.5 percent to $396 million. All of the 12 major commodity groups carried by the railroad's freight cars contributed to higher revenues for the year, although Crane said "some did so only because of freight rate increases which took effect during the year."

New automobiles and parts, construction materials and petroleum products declined in actual volume but brought in higher revenues because of rate hikes, for example. Coal shipments increased in volume by 27 1/2 percent and chemical shipments increased more than 20 percent.

Union Trust Bancorp, a $1.3-billion-asset Baltimore-based holding company for Union Trust Co. of Maryland, reported 1979 operating profits before securities transactions of $8.9 million ($3.63 a share) compared with $8.4 million ($3.41) a year earlier. Fourth-quarter operating profits dipped to $2.1 million (86 cents) from $2.2 million (90 cents), reflecting the impact of government credit-tightening measures in the final months of the year.

Chairman J. Stevenson Peck said loan volume increased more than 10 percent in the year to $815 million, while higher interest rates boosted loan income 23 percent. Assets rose more than 8 percent during 1979.

MCI Communications Corp. of Washington reported earnings of $8.1 million in the nine months ended Dec. 31, almost double the $4.3 million level of the previous comparable period. Revenues jumped 49 percent to $101 million for intercity communications firm.

Earnings per share were affected for the first time by preferred stock dividend requirements related to offerings at the end of 1978. For the nine months, per-share profits were decreased to 10 cents from 15 cents.

Flow General Inc., a McLean manufacturer of biological and medical products and broadcast equipment, reported profits of $1.5 million (86 cents a share) in the six months ended Dec. 31 compared with $1 million (63 cents) a year earlier, when fewer shares were outstanding. Sales rose 27 percent to $34.6 million.

American Realty Trust, an Arlington real estate investment trust, reported a loss in the year ended Sept. 30 of $365,321 compared with year-earlier profits of $1.76 million (79 cents a share), which had included a $840,000 tax benefit equal to 38 cents a share. Revenues increased to $6.1 million from $6 million, but ART set aside $2.1 million for possible losses in the recent year. A one-time gain from a real estate sale netted more than $1 million for the trust in fiscal 1979.