A finite element method is presented for free vibration analysis of thin plates subjected to complex force systems applied in the middle-plane of the plate. The equation of motion is characterized by the basic stiffness, consistent mass, and incremental stiffness matrices. The method is demonstrated by using both a conforming and a non-conforming rectangular plate element. Numerical examples of free vibration of plates under various inplane loadings for different aspect ratios and edge support conditions are illustrated. Particular attention is given to the influence of load intensity on the natural frequency of vibration and the extrapolated load corresponding to zero frequency which yields the static buckling load. It was found that in most cases the relationship between the square of the frequency and the load is not linear. The finite element solutions were also made for a sequence of gridwork refinements to show the convergence characteristics. Comparison of the natural frequencies (zero middle-plane load), the buckling loads and the frequency-load relationships with known analytical and numerical solutions indicates that the method gives good results even for relatively few elements.