On mail-in ballots, tallied Wednesday, members of the Society of Professional Engineering Employees in Aerospace also voted by more than 3 to 1 to authorize their leaders to call a strike, should it become necessary.
Contract talks may resume in a week or so, possibly with participation of a federal mediator, Boeing spokesman Peter B. Conte said.
Union spokesman Bill Dugovich said the employees would continue working under terms of the contract that expired Wednesday "until a new agreement is reached or an impasse is declared."
The rejection vote was 5,562 to 127, or 98 percent against the offer in the union's engineering unit, and 4,733 to 60, or 99 percent in the technical unit.
The rejected offer would have required the workers in question to pay 10 percent of their medical premiums beginning in 2001. Early retirees would have lost medical benefits, and Boeing could have required weekend work without overtime pay.
The union's engineers and scientists are not expected to strike. While such a labor action could impede production, it would not shut it down.
The union's highest previous vote against a contract offer, 71 percent in 1992, was followed by a one-day walkout - the only strike in the union's history. Boeing refused to budge at the table, and union members later voted to accept the same offer they had rejected.
But earlier this year the company's biggest union, the International Association of Machinists and Aerospace Workers, ratified a contract after Boeing gave in to most of its demands.
Conte would not say whether the company would sweeten its offer when the two sides meet again.