Striking machinists overwhelmingly ratified a new three-year contract with United Airlines yesterday, and United officials said partial operations will resume Monday.

The 3-to-1 vote in favor of the new contract ended a walkout by 18,600 mechanics that grounded the nation's largest domestic air carrier for 55 days and created travel havoc for hundreds of thousands of air passengers.

To win back business lost during its nearly two-month shutdown, which cost the airline $1.5 million a day, United announced a special discount program, atop a cut-rate fare announced earlier for some coast-to-coast flights.

The union ratification followed rank-and-file rejection of two previously negotiated contracts and sanctions wage-and-benefit gains well above President Carter's 7 percent wage and benefits guideline, although the contract technnically may be exempt from the standards.

The settlement, reached in Denver after 11 days of intensive negotiations, calls for an increase in base hourly pay from $10 to $13 over three years, or 30 percent, plus benefit gains and cost-of-living adjustments.

Government officials said they will study the contract next week to determine whether it is a "tandem" settlement, based on a Trans World Airlines pact negotiated before the guidelines were announced last fall, and thus not covered by the 7 percent restriction.

United which normally carries 130,000 passengers on 1,600 flights a day, said it will restore one-quarter to one-third of its service Monday and the rest within 10 days. Reservations and ticketing functions were to start immediately.

For the Washington area, officials said, 14 of 33 flights will operate out of National Airport Monday, along with seven of 14 from Dulles and six of 19 out of Baltimore-Washington.

Under the discount program, which Unted Officials said was approved late yesterday by the Civil Aeronautics Board, Passengers flying with United from May 28 to June 17 will receive coupons good for 50 percent discounts on future domestic flights through Dec. 15.

The coupons will be good for all flights within the continental United States and for roundtrip flights originating in Hawaii, officials said. No special scheduling restrictions will apply they added.

The earlier come-back inducement is a $108 one-way fare for five daily nonstop flights between New York and Los Angeles and a single night flight between Newark and San Francisco. The regular one-way fare between these cities is now $236, although some special round-trip fares with restrictions can go as low as $216 for midweek night flights.

A United official described the 50 percent discount as unprecedented for the airline industry, and said it could cost "millions of dollars," depending on how extensively it is used.

Other airlines quickly began clambering aboard the latest rate-cutting bandwagon, with American announcing that it will match both of United's new programs and TWA saying it will match the $108 fare on all its New York-Los Angeles flights starting June 7.

United officials said they anticipate no problems "depickling" their planes for flight because they have been undergoing constant service by nonstricking supervisory employes. The main problem, they said, is reassembling crews.

According to one bargaining source, the improvements won in the third round of negotiations came largely in the area of cost of living adjustments, pensions and mealtime pay, for an overall contract cost increase of 44 percent over three years, instead of 42 percent in the previously rejected pacts.

Cost-of-living increases, for instance, will provide up to a maximum of 13 cents per hour for each of three annual increases. Pensions were fattened and tied to the cost of living, and a paid half-hour lunch was provided for all workers, instead of just those on the night shift.

Government officials said they understood the total settlement cost was more like 29 or 30 percent, but wanted to check more thoroughly before deciding whether it runs afoul of the guidelines.

The guidelines program has already been stretched by the rencent Teamster settlement, and its penalty provisions are under attack in federal court by the AFL-CIO.