SPH is a Lagrangian based computational method that can be used for solving fluids and solid mechanics problems. In this work, SPH is utilized to solve the two dimensional Navier’s equation for linear elastodynamics problems. The SPH technique computes the discrete particle properties using a smoothing distribution function, which takes into account the effect of neighboring particles. To investigate the performance of the developed method in solving solid mechanics problems, the problem of plate bending was simulated. The results show good agreement between the simulation and analytical solution. Additionally, the study found an indication that the current method of enforcing boundary conditions produces boundary effects at locations where the plate is attached to the wall and at the end of the plate.