The power series polynomial constraining method is proposed in this paper. The dynamical model of the cantilever plate can be established by applying the constraint, which is different from the traditional polynomial. Firstly, the characteristic orthogonal polynomial was used to describe the displacement field of the rectangular plate of which all edges are free. Then the four-sided free plate was equivalent to cantilever plate by power series multiplier constraint method. The characteristic equation of the constructed cantilever plate was obtained by the Rayleigh–Ritz method. Natural frequencies and modal shapes of the plate were obtained by solving the characteristic equation. Next, the proposed method was adopted to establish dynamical model of a pair of solar panels clamped on the central platform symmetrically. The convergence of the proposed method was verified by comparing the calculated results of the cantilever plate with that of the finite element software ANSYS 15.0. The optimum order the power series polynomial was obtained by comparing different results. The analysis of the dynamical characteristics of the cantilever plate and the spacecraft demonstrates the validation of the proposed method. This method can provide a new idea for the plate with local edge constrained.