Abstract: Based on the principle of virtual work and the differential equation similarity of the free vibration to the elastic curved surface of sheet in both expression and mechanics, the inertia force due to sheet vibration is regarded as the transverse load to bend the sheet, and the reciprocal theorem of work done is used to solve the dynamic problem, thus obtaining the formula of natural frequency of sheet. Setting an appropriate vibration mode shape function, the natural frequency of simply-supported sheet in shape of isosceles right triangle or equilateral triangle is solved via the reciprocal theorem of work done, mapping and superposition. The method combining statics with the reciprocal theorem of work done to solve dynamic problems is easy to extend, and it is simple with high accuracy in solving the natural frequancy of a structure.