The present work mainly reports a significant development of a novel efficient meshfree method for vibration and buckling analysis of orthotropic plates. The plate theory with orthotropic materials is followed the Kirchhoff"s assumption in which the only deflection is field variable and approximated by the moving Kriging interpolation approach, a new technique used for constructing the shape functions. The moving Kriging technique holds the Kronecker delta property, thus it makes the method efficiently in imposing the essential boundary conditions and no special techniques are required. Assessment of numerical results is to accurately illustrate the applicability and the effectiveness of the proposed method in the class of eigenvalue problems.