In this article, complex differential quadrature method based on differential quadrature method in the real domain is proposed for potential and plane elastic problems. By use of Lagrange interpolation in the complex plane instead of boundary integral formulation, the method is free of singularity. The use of collocation ensures that the boundary conditions are exactly satisfied on the boundary. The method is applied to some potential and plane elastic problems. Numerical results obtained by the present method are in good agreement with either analytical solutions or finite element results.