Union Pacific Corp. and Missouri Pacific Corp., two of the nation's financially strongest railroads, announced yesterday that their directors have agreed in principle to merge.

The billion-dollar merger proposal would create a railroad system that would be the third largest in the country, assuming approval of two other proposed railroad mergers pending at the Interstate Commerce Commission.

The Union Pacific, which pushed west more than a century ago, now operates 9,700 miles of track in 13 western states stretching from Los Angeles and the Pacific Northwest east to Kansas City and Omaha. The Missour Pacific operates 11,500 miles of track in 12 states, stretching from Chicago and Omaha in the Midwest as far west as Pueblo, Colo., and El Paso, Texas, and south to Brownsville, Texas, and New Orleans.

The two lines connect in Kansas City and Omaha, and a merger would provide the western Union Pacific with a direct link to major Gulf ports.

Besides the rail lines, however, both Union Pacific and Missouri Pacific are large holding companies with sizable operations outside the railroad sphere whose combination would be "a hell of a big merger," one railroad expert said yesterday.

Union Pacific Corp. had total revenues of almost $3 billion in 1978, ranking it third in that category among the nation's transportation companies.

Union Pacific consists of four operating companies: the railroad; Champlin Petroleum Co., which engages in exploration, development and production of crude oil and natural gas, and refines and markets petroleum products; Rocky Mountain Energy Co., which develops UP's reserves of coal, uranium and trona and explores for minerals; and Upland Industries Corp., which manages and develops a land bank of prime industrial and commercial sites.

Missouri Pacific was the 13th largest transportation company in 1978, when its consolidated revenues were $1.7 billion.

Missouri Pacific owns the Mississippi River Transmission Corp., which operates a 1,600-mile natural gas pipeline system and is engaged in gas exploration and production.

Top officials of the two corporations said the proposed merger would result in a stronger railroad but also touted its benefits in the area of natural resources and energy.

"The move will firmly position the two railroads for the future and create a strong central core to the nation's rail system," said James H. Evans, chairman of Union Pacific. "It will also, in our opinion, make a constructive contribution toward meeting the nation's energy needs by providing more efficient long-haul single-line coal transportation over the combined systems, as well as offering efficiencies arising out of coordinated operations."

The proposed merger is subject to the execution of a definitive merger agreement, approval of the shareholders of both companies, the receipt of a favorable tax ruling, and the approval of the ICC, which has 31 months by law to decide on it after a formal application is submitted.

Under the merger proposal outlined yesterday, each common share of Missouri Pacific would be converted into 0.55 common share of Union Pacific and 0.275 share of a new convertible preferred stock of Union Pacific once the merger is consummated.

The new preferred stock would be convertible into common on a share-for-share basis and carry a cumulative annual dividend of $7.25. As of Dec. 31, 1979, Missouri Pacific had about 15.8 million common shares issued and outstanding.

The two companies rate among the top three or four strongest railroads in the country, anaylsts say. Union Pacific had profits of $264 million in 1978. Its rail revenues totaled $1.5 billion. Missouri Pacific had rail revenues of $1.2 billion in 1978; profits that year totaled $130 million.

Officials of the two companies say the merger would create the third largest rail system in the nation. The combined Burlington Northern and Frisco, now awaiting ICC approval, would be the largest with 29,600 miles of track. The combined Chessie System/Seaboard Coast Lines, also awaiting ICC approval, would be the second largest with 26,600 miles of track.