The growing numbers of passengers using Eastern Airline's Air-Shuttle service between Washington and New York will find it easier to catch a flight this fall when the airline begins using larger planes on the heavily traveled route.

The four 107-passenger McDonnell Douglas DC5s currently used on the route will be replaced by brand-new 177-seat Boeing 727-200 aircraft, Eastern officials said, significantly increasing capacity on the shuttle schedule. It is the first time new aircraft have been ordered for the guaranteed seat service.

The seven DC9s used as back-up planes when the first plane is filled will also be replaced by 727s, although seating will be about the same as the DC9s they replace.

Eastern hopes the change will cut down on the waiting time some passengers experience as well as the number of extra flights it has to make.

Traffic on the shuttle has been booming this year. In 1973, the shuttle, operating between Washington/New York and New York/Boston, carried 2.6 million passengers, up 8.4 percent from 1977. For the first six months of this year, shuttle business was up by 24 percent overall, and higher than that on the Washington-New York segment.

Eastern officials cite reluctance of travelers to drive, increased use of the Boston airport as an international gateway, and such temporary phenomena as the United Airlines' strike and the grounding of the Dc10s as reasons for the increased traffic.

Another factor may be the reduced number of flights being offered by American Airlines and National Airlines between Washington and New York. American, which used to offer six flights a day in each direction, cut the schedule to three a day in June. An American spokesman said the reason was a desire to use the planes elsewhere.