Dade County has become the latest metropolitan area to join the rush to rapid rail transit, beginning construction this month of a 20.5-mile above-ground system.

Transportation officials here believe that the system, called Metrorail, will be ready for business in 1984. It will connect residents in the most densely populated areas of the county with downtown Miami.

Metrorail will cost taxpayers $867 million, as compared to $7 billion for the 101-mile Washington Metro system. Dade County also wants to build a downtown "people mover," covering 1.9 miles, at an added cost of $76 million.

The federal government will pick up most of the tab. Dade County already has received a pledge from the Urban Mass Transit Administration for more than 75 percent of the money -- $670.6 million -- and has applied for $41.6 million for the people mover.

The rest of the money will be supplied by the state of Florida, Dade County and the cities of Miami and Hialeah.

Miami, like Los Angeles, is a car-oriented city. Last year, 1.2 million autos were registered in Dade County by a permanent population of 1.5 million.

But Metrorail will not reach everyone. Miami Beach will not be on the system, though the county offered to build a line over Biscayne Bay to the beach.

"Beach residents were adamantly against it," said Orrie Strubinger, spokesman for the county transportation department. "They thought we were going to tear down the Third Avenue El in New York and rebuild it on the beach."

Metrorail will not serve residents in northeast Dade County, either, or commuters in Broward County to the north.

However, its planned 20 stations will serve riders living around Coconut Grove, Coral Gables, the University of Miami and Hialeah.

Bus service also is expected to improve in the county. The county plans to almost double its number of buses -- now about 500 -- to cover territory that Metrorail will not serve. No one in the county will be farther than five blocks from a bus stop, officials say.

Miami has studied Washington's Metro system, and there are similarities between the two cities' rapid transit systems. But there also are major differences.

"Our system will be spartan in comparison to yours," Strubinger said. Stations basically will be concrete overhangs above street level. There will be no Farecard system -- too confusing and too susceptible to breakdowns, Dade county officials say -- and all rides will cost the same.

"We will charge whatever 50 cents is worth in 1984," Strubinger said. The people mover, described as a horizontal elevator, will cost the 1984 equivalent of a quarter.

The rail system is expected to be open seven days a week for 20 hours a day, she said. Unlike the Washington system, no Metrorail stations will open until all stations have been completed.

Other differences are a result of geography and climate. Miami's high water table prohibits an underground rail system. And the system's cars will be stainless steel rather than aluminum, which Washington bought, because aluminum corrodes in the Florida climate.

Dade County officials believe 250,000 to 300,000 people will ride Metrorail daily, but they expect to lose $24 million a year on the county's public transportation system.

They expect the system will save 13 million gallons of gasoline a year, however, and "if gas costs $2.50 a gallon by 1984," Strubinger said, "then we may not lose what we anticipate losing."