The present work deals with obtaining the critical buckling load and the natural frequencies of clamped, orthotropic, rectangular thin plates subjected to different linear distributed in-plane forces. An analytical solution is proposed. Using the Ritz method, the dependence between in-plane forces and natural frequencies are estimated for various plate sizes, and some results are compared with finite element solutions and where possible, comparison is made with previously published results. Beam functions are used as admissible functions in the Ritz method.