Abstract: This paper deals with the in-plane free vibration of rectangular plates in arbitrary boundary conditions via the improved Fourier series method (IFSM)． In the investigation，first，the admissible functions of the plate dis-placement are expressed as an improved Fourier sine series to overcome the relevant discontinuities or jumps of elas-tic boundary conditions． Then，the unknown expansion coefficients of the admissible functions are considered as generalized variables and are determined by using the Ｒayleigh-Ｒitz technique combining with the energy functional based on the energy theory． Thus，the common in-plane vibration problem is converted into a standard eigenvalue problem． Finally，the results of rectangular plates in various boundary conditions are presented and are compared with those in the literature and with those obtained by the finite element method． It is found that the proposed method is of strong reliability，good convergence and high accuracy．

Key words: rectangular plate, in-plane vibration, improved Fourier series method, arbitrary boundary condition