Richard D. Simmons, president of The Washington Post Co., said yesterday that the company, already headed for a vigorous financial showing in 1984, also will see continued strong earnings growth in 1985.

"In a period when uncertainties are rising about the enduring strength of some media, the particular mix of Washington Post Co. properties, resources and investments for the future make our prospects better than ever," Simmons told a meeting of security analysts in New York.

The Washington Post newspaper is having a banner year, Simmons said. Operating income will be ahead of 1983, and operating margins, which were up 19.7 percent last year, will rise again in 1984, he said.

Gains were predicted for the four Post-Newsweek stations. Operating income, running at the $50 million level for 1984, is double the figure of three years ago, Simmons said. The stations' margins, which were 36 percent in 1983, are expected to go up for both 1984 and 1985.

Simmons said that Newsweek's 1984 financial results would be up over 1983, and he predicted an even better showing in 1985.

"The combination of rising ad pages, improved business performance and superior editorial coverage has positioned Newsweek to be the hot magazine of the mid- and late 1980s," Simmons said. He said that Newsweek's long-term margin goal was 12 percent. The margins currently are 8 percent, before corporate charges and adjustments.