The Federal Communications Commission was inundated yesterday with hundreds of applications from companies seeking government permission to offer a brand new portable telephone service in some of the nation's biggest cities.

When the final count is tallied sometime today, FCC officials expect to have about 400 applications for cellular radio systems, which use computers and low-power transmitters capable of carrying thousands of conversations simultaneously on a mobile-phone system.

Last June, nearly 200 applications were filed to offer cellular radio in the nation's top 30 cities. The 400 applications filed yesterday are for cellular radio systems in the nation's second largest 30 cities, including Richmond and Norfolk.

FCC officials attributed the sharp increase in applications to the growing belief that this new service will be highly profitable, with thousands of businessmen and consumers demanding portable telephone service. Several large corporations that hadn't applied in the first go-round applied yesterday, including Time Inc. and United Brands.

Additionally, they said the increase in applications may stem from the fact that it is less expensive to build a cellular system in a smaller city.

The FCC now predicts the agency will begin considering them until the beginning of 1983 -- at the earliest.