Introducing a pressure variable, governing equations of elasticity are expressed as displacements and pressure coupled system of partial differential equations. Barycentric interpolation is applied to approximate unknown functions. Matrix-vector forms of discrete expressions of governing equations for plane elastic problems are obtained by using barycentric interpolation differentiation matrices. Discrete boundary conditions of displacements and pressure are obtained by using barycentric interpolation. Boundary conditions are imposed by additional method to form an over-constrained linear algebra equation system of plane elastic problem. Numerical solutions of displacement for plane elastic problem are solved with least-square method. Numerical examples illuminate efficiency and computing precision of the method.