Exact vibration results for a cantilever plate using the thin isotropic plate bending theory are not known. The best separable function approximation of the vibration mode can be obtained by reducing the plate partial differential equation to two simultaneous ordinary differential equations and their boundary conditions. Imposing the boundary conditions, this analysis can be simplified to the solution of four non-linear algebraic equations in four unknown modal parameters. An investigation of the theoretical and numerical aspects of this vibration analysis of the cantilever plate is presented, and the results show that the modal parameters are sometimes imaginary. The strong dependence of the vibration frequencies and modal parameters on the Poisson ratio is a characteristic feature of plates with free edges.