In this research, a new method based on the method of fundamental solution has been proposed for eigensolution of partial differential equation (PDEs) with constant coefficient. The first set of results has been presented for the Helmholtz equation. In this method, the approximate solution is expressed as a series, using exponential functions as the fundamental solution. Constant coefficients of this series are evaluated through an especial discrete transformation. In this research after introducing an especial flexibility matrix, a new criterion was proposed for evaluating eigenvalues and eigenmodes. After developing an algorithm for eigensolution of the Helmholtz equation, this algorithm has been extended to other important eigenequations in solid mechanics including free vibration of plates and buckling of plates.
