The transient response of a simply supported layered cylinder made of a three-phase magneto-elecrolastic (MEE) composite, consisting of an elastic matrix reinforced with piezoelectric and piezomagnetic fiber has been studied by developing a semianalytical finite element method employing fourth-order Runge-Kutta method. Numerical results are presented for different volume fractions of piezomagnetic fiber in a three-phase MEE material with simply supported boundary conditions. A study of the transient responses of (PZT)-epoxy mixed component (PECP), (Terfenol-D)-epoxy mixed components (MSCP), barium titanate (BaTiO3) and a two phase magneto-electro-elastic layered cylinder, under simply supported boundary conditions has also been presented. A comparison between the elastic and the coupled responses of the MEE cylinder is presented as well. Ansys 8.1 is used to validate the present code for the response of cylinder made of PECP and MSCP materials.