The numerical solution of the 2D linear elasticity problem numerically from the given body and traction forces, Poisson ratio, and Young's modulus is investigated. A continuous linear finite element method is adapted to solve the forward elasticity problem when Young's modulus is defined as a variable valued function. The body's deformation is approximated by applying an approximation of the plane stress condition. We have studied the convergence analysis of the proposed linear elasticity problem. A numerical example presents the worthiness of the proposed technique. Keywords: Linear elasticity problem, Elastic properties (Young's modulus and Poisson's ratio), Convergence analysis, Finite element method.