In this paper, a layer-wise finite element formulation is developed for the analysis of a functionally graded material (FGM) cylindrical shell with finite length under dynamic load. For this purpose, FGM cylinder is divided into many sub- layers and then the general layerwise laminate theory is formulated by introducing piecewise continuous approximations through the thickness for each state In this model the radial displacement is approximated linearly through each "mathematical" layer. The properties are controlled by volume fraction that is an exponential function of radius. The governing equations are derived from virtual work statement and solved by finite element method. The main contribution of the present study is to develop a discrete layerwise finite element for a 2- dimensional thick FGM cylindrical shell. Results are obtained for the time history of the displacement and stress components with different exponent "n" of functionally graded material. In addition, natural frequency and mean velocity of the radial wave propagation for different exponent "n" of functionally graded material (FGM) are studied and compared with similar ones currently obtained for FGM cylindrical shell of infinite length.