Officials of Southern Railway Co. say they feel unappreciated by a general public that associates railroads with inadequate and financially struggling passenger. service.

But Southern runs an enormously successful railroad, operating more than 10,000 miles of track across the generally thriving Southeast at a time when freight service is viewed as an energy-efficient way to transport goods.

Last year alone, the Washington-based company earned $127 million, making it the nation's second-most-profitable railroad.

Stock analysts give the company's management only the highest marks and predict a rosy future for a railroad that has managed to keep its labor costs low and that, through its own initiative and the many factors that make the Southeast a sound place to do business, continues to thrive.

But Southern President Harold H. Hall says his line and those of his competitors in the railroad freight business generally are not recognized for their success. Hall by all accounts will succeed L. Stanley Crane as Southern board chairman next year when Crane hits the company's mandatory retirement age of 65.

As Hall views it, the general public includes Southern in their image of the morass of the nation's rail passenger service. Southern, however, got out of the passenger business last year when it sold its Southern Crescent service to Amtrak.

"I don't think the American public perceives railroads as a part of the American industrial situation," Hall said recently. "They think we're outmoded and that we don't use modern technology.

"To the general public, railroads mean passenger trains. It grieves me that the public doesn't recognize us," he continued. "We're guilty of not getting our message across, and the news media is somewhat guilty because what gets the publicity is the unusual and catastrophic."

But the fact of the matter is that Southern not only is successfu. It is a computerized and seemingly modern company that most railroad observers feel is as solid a railroad as any in the country.

Recently about 50 financial analysts and Southern officials toured selected parts of the company's system. Their conclusions, drawn from a three-day luxury trip, are that contemporary technology, an ability to read the future and plan accordingly, and an effort to allocate the company's profits to continual upkeep of track and equipment have kept Southern in its apparently solid financial situation.

Take as an example the coal transloader that Southern operates in Pride beside the Tennessee River on a 390-acre plot. It is the only facility in the Southeast that takes coal directly from barges and quickly places it in railroad coars. About six million tons of coal will move through the site this year for delivery to the Southern Co., a holding company for five utilities in the region. It is estimated that the Southern's revenues from the Pride facility will be about $3 million this year. By 1981, the transloader will handle about 7 million to 8 million tons of coal.

The coal is shipped from mines in southern Illinois and eastern Kentucky by rail to bargeloading sites on the Tennessee, Ohio, and Mississippi rivers. At Pride the coal not only is transferred from barge to rail car, but also is mixed to provide a variety of blends depending on the sulfur content required by the power company.

Built at a cost of about $15 million, the series of huge conveyer belts can move about 5,000 tons of coal an hour. Although the site was put into operation only four years ago, it is close to 50 percent capacity and may be close to full capacity by 1985 if plans to increase coal use across the country remain intact.

Although Southern officials did not know precisely what they would do with the land when they bought it in 1966, they sensed its location by the river and adjacent to a main track line would prove valuable.

Similarly Southern has continued an aggressive program of trying to bring new businesses along its track such as a $271 million, 1,600 acre Miller Brewing Co. site in Eden, N.C., selected by officials of Miller and its parent company, Philip Morris Inc.

The plant employs some 1,500 workers and can produce about 8.8 million barrels of three brands of Miller beer a year. For Southern, the Miller plant already represents $24 million a year in revenues; most of the beer leaves Eden on Southern cars.

Thus at a time when industrial growth is limited, Southern is expanding its operations, including the opening of a major, highly computerized 50-track rail yard at Linville, N.C., that cost $48 million to construct. Southern officials believe the Linville car-handling yard, the company's seventh, may be the most modern in the country.

By most yardsticks, Southern prospects would appear rosy. In the third quarter of this year, profits increased by 73 percent to $40.7 million. And for the most part, stock analysts see only good times for Southern.

Analysts noted the company's fuel inventories are high, management is qualified and has a mix of youth and experience. and the company continually pumps money into maintaining its equipment -- particularly its tracks and locomotives.

Yet Southern officials cite several factors when expressing some caution about the railroad's future. Like their counterparts in any business, they are concerned over the short-termed economic prospects for the country. They particularly worry about the possibility that enactment of railroad deregulation legislation could force them into joint rates.

"Conrail could ruin our rates," Crane said, noting that if Conrail is free under deregulation to raise its rates at will, Southern customers will wind up footing the bill.