This paper deals with a new method for analysis of lateral vibrations of flat plates of various shapes. A general solution is derived as a linear combination of particular solutions of the governing equation. To determine the natural frequencies and the natural modes, the collocation method and the method of virtual work are used. Programs for computation are very simple because of simplicity of the basic principles. The natural frequencies of circular, elliptic, square and rhombic plates with clamped edges and square and rhombic plates with free edges are calculated as numerical examples. The results agree well with the exact values or the values which have been obtained so far by various methods of approximation. This method may be used not only for plates of various shapes and with various boundary conditions but also for structures containing plates as elements.