Abstract: Aiming at the fundamental frequency analysis of discrete-clamped elastic plates with multi-concentrated mass, with the help of the small deflection elastic deformation plate theory and the energy method of Rayleigh-Ritz, the paper determines both the vibrating energy function and the modal function of discrete-clamped elastic plates with multi-concentrated mass. Based on the analysis of boundary conditions of discrete-clamped points of elastic plates, the vibrating mode function for fundamental frequency of the discrete-clamped elastic plate is presented, meanwhile by the energy extreme method, both the interpolation coefficients of fundamental vibrating mode function and its fundamental frequency varying with the change of the size and positions of Multi-concentrated mass are analyzed. The feasibility of the analytic method is illustrated through an application to the discrete-clamped elastic plate without multi-concentrated mass, and the analysis results are compared with those of the finite element method. In addition, taking rectangular elastic plate with two concentrated mass as an example, for all fundamental mode shape functions, the paper performs the description and analysis of interpolation coefficient k and the fundamental frequency f varying with the change of the size and positions. The above analytical method can provide a feasible theoretical basis for the dynamic design of the printed circuit board (PCB) in practical engineering.