A computational technique based on domain-boundary element method (D-BEM) is developed for elastodynamic analysis of functionally graded thick-walled cylinders and annular coatings subjected to pressure shock type of loadings. The formulation is built on the wave equation, which is derived in accordance with plane elastody-namics. Weighted residual statement for the wave equation is expressed by using the static fundamental solution as the weight function. Applying integration by parts and incorporating the boundary conditions, the problem is reduced to an integral equation. Problem domain is discretized by quadratic cells to transform the integral equation into a system of ordinary differential equations in time. Equation system is solved numerically applying Houbolt's method. Developed procedure is verified through comparisons to the analytical results available in the literature. Parametric analyses are carried out considering short-time ramp and exponential variation types of pressure shocks. Presented numerical results illustrate the influence of material property gradation on time histories and spatial distributions of displacement and stress components in FGM thick-walled cylinders and annular coatings.