Abstract: This paper presents presents a new analytical solution of transverse vibration of rectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way.The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate.The analytical solution of the differential equation of motion of the rectangular plate,which includes the unknown reaction forces.is gained.The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and the transverse displacements of the plale along the elastic line supports.There presentations of foe frequency equation and the mode shape functions are different from those obtained by other methods.