In this article, the propagation of elastic wave is studied in two dimensional functionally graded thick hollow cylinder with finite length subjected to mechanical shock loading, considering two dimensional variations for mechanical properties. The meshless local Petrov-Galerkin (MLPG) method is developed to solve the boundary value problem. The Newmark finite difference method is used to treat the time dependence of the variables for transient problems. The FG cylinder is considered to be under axisymmetric conditions. The mechanical properties of FG cylinder are assumed to vary across thickness and length of FG cylinder in terms of two dimensional volume fractions as nonlinear functions. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a Heaviside test function. Nodal points are regularly distributed along the radius and length of the cylinder and each node is surround ed by a circular sub-domain to which a local integral equation is applied. The wave fronts of displacements are illustrated for various values of volume fraction exponents in 2D domain at various time intervals. The 2D propagation of elastic wave can be tracked through radial and axial directions in 2D functionally graded cylinder.

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