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Starting from the integral forms of the equilibrium condition and the constitutive law over the small volumes centered at the nodes, this study approximates stresses and displacements independently by means of the meshless approximation. By interpreting the meshless approximation from a new perspective, the procedure does not need to differentiate the nodal shape functions. The stresses can be approximated as accurately as the displacements, even if the shape functions for the stresses and the displacements are both taken as those simple interpolation functions such as the Shepard functions. Besides, in general no background mesh is needed. Illustrated by some elastic–plastic problems, the procedure enjoys high efficiency and excellent numerical properties.