The presidential election is over but in the U.S. agricultural community another campaign is under way, complete with issues, behind-the-scenes lobbying and two candidates. It is the campaign for secretary of agriculture and it will end only when the new president casts his vote.

Illinoisan John R. Block, a successful large-scale commercial farmer and the state's top agricultural official, jumped out to an early lead in the political handicapping after picking up support from Sen. Bob Dole (R-Kan.) and other influential members of Congress.

But in the last two weeks the grain trade and some big farm copperatives have marshalled support for Richard Bell, executive vice president of Riceland Foods, an Arkansas co-op with sales of rice, soybeans, meal and vegetable oil totaling more than $600 million a year.

Block's supporters are calling it a race between a man with roots in the soil and the concerns of farmers at heart and a man who represents agribusiness and the trade. Bell, who had no comment yesterday about possible approaches from the Reagan team, responded that his credentials include growing up on an Illinois farm and working for the interests of farmers while employed at the Department of Agriculture from 1959 to 1977.

This week, Gov. John Carlin of Kansas, a Democrat and chairman of the agricultural committee of the National Governors Association, sent a telegram to President-elect Ronald Reagan endorsing Block. Joseph Kinney, the committee's staff director, said that Block had the support of "every Republican governor."

In the telegram Carlin told Reagan that Block "met the criteria" of having a farm background.

"There's a lot of concern on the part of the governors that the next secretary have sensitivity and awareness about soil conservation, research, extension work and transportation. John Block started a soil conservation service, a farmland preservation program, and was one of the most innovative state secretaries of agriculture. It's obvious to anyone that Bell doesn't have experience in these areas," said Kinney.

Two weeks ago, Dole, who will serve on the Senate Agriculture Committee as well as chair the Senate Finance Committee, said he backed Block as "a producer who does not represent any particular group within agriculture."

In a telephone interview Block said that he favors increasing loans rates, or floor prices, for farm products. Block said he believes the present floors are below the cost of producing the food.

Meanwhile, Bell has picked up support from Glen Hofer, vice president of the National Council of Farmer Cooperatives. Hofer was quoted last week as saying that Bell was "absolutely trade-oriented -- he knows all the players."

Sources here said yesterday that officials of several major grain trading companies have indicated they support Bell.

Last week, the Des Moines Register reported that the inspector general of the Department of Agriculture was reviewing a complaint that Riceland had falsified documents to qualify for assistance as a small business. Bell said yesterday he had no knowledge of this, but he confirmed that Riceland was one of "some 40 companies" that had been subpoenaed by the Justice Department to provide information in connection with an investigation of industry pricing and marketing practices.

Riceland Foods, in Stuttgart, Ark., is a cooperative owned by its 25,000 farmer members. Its business centers on buying members' soybeans and rice, processing, milling or bagging their out-put, and selling the products in Europe, the Middle East and the Caribbean.

In his 18 years at the Department of Agriculture, Bell concentrated on foreign trade. He served as an agriculture attache in Canada in 1963 when the Soviet Union made its first huge purchases in that country. He then moved to Brussels, where he was present in the formative years of the Common Market and where he reported home on developments in the grain trade, European food policy and farm matters.

From 1968 until 1977 he was promoted steadily, rising from director of the grain division to assistant secretary of agriculture for international commodity affairs. In these capacities he was involved in most of the major policy decisions concerning grain sales to the Soviet Union.