Abstract: The meshless local Petrov-Galerkin(MLPG) method applied to the bending problem of orthotropic plate on elastic foundation was investigated.The method was based on classical plate theory and used the moving least-squares approximation to interpolate the deflection function.In the analysis,the essential boundary condition was applied by the penalty method.The discrete linear equation employed a local symmetric weak form of control differential equation of orthotropic plate on the elastic foundation.Two numerical examples illustrated that the meshless local Petrov-Galerkin(MLPG) method was easy to use and with high accuracy for solving the bending problem of orthotropic plate on elastic foundation.