In this study, dynamic bending of FG circular and annular plates with stepped thickness variations is examined. System of governing differential equations are derived based on the first order shear deformation theory and solved by using a semi-analytical method based on the power series and the fourth-order Runge–Kutta methods. On the basis of presented solution procedure, dynamic behavior may be obtained for the plates under various dynamic loads such as stepped, stepped pulse, triangular pulse and harmonic loads which can be imposed on the arbitrary parts of plates. Also, transverse asymmetric plates with various stepped segments with various boundary conditions may be analyzed. For derivation of system of governing differential equations, Stepped annular plates are divided into multiple constant thickness annular segments and stepped circular plates are divided into multiple annular and one circular segments with constant thickness. Governing equations are written for each segment, individually. Then, continuity conditions of displacements and stresses are imposed between various segments. Comparisons made with results of a numerical finite element code (ABAQUS software) on the basis of the three dimensional theory of elasticity reveal that the obtained results by using the proposed solution procedure have very good accuracy for various stepped plates under various dynamic loads.