This paper deals with the problem of free vibration and buckling of rectangular plates subjected to non-uniform normal in-plane loading. At first, the governing equation has been derived and solved for the free vibration and buckling of the plate, by using power series solution. In this way, the natural frequencies of plates for various type of loading have been estimated. As a result, the buckling critical loads have been obtained when the value of natural frequencies approaches zero. In order to have a comparison between the obtained results and those of analytical solutions, the problem has been analytically solved for a specific type of loading. Finally, the effect of the various parameters has been investigated.