The element free Galerkin method is used to analyze free vibration of thin plates resting on Pasternak elastic foundations with all possible types of classical boundary conditions. Convergence of solution is studied by increasing number of nodes for different boundary conditions and foundation parameters. Upon comparison with available results in literature, it was found that the method converges very fast and has very good accuracy even with small number of nodes. Applicability of the method was shown by solving numerical examples with all possible combinations of boundary conditions and different values of foundation parameters.