In this thesis the tow-dimensional wave propagation in a functionally graded elastic medium is considered. It is assumed that the stiffness and density of the medium vary continuously in one direction. This work presents analysis in both time and frequency domain. In time domain, a graded element is presented for static and dynamic analyses in FGMs. This element clearly simulates wave propagation in inhomogeneous materials. The most important property which an element must have to be reasonable in wave propagation analyses in FGMs is simulating reflection only from boundaries. In frequency domain a dynamic stiffness matrix is generated using stiffness and mass matrix used in time domain...