Porous solids are less stiff than the solid, but its stiffness can be increased if the elastic properties of the struts within are sterically stiffened. The stiffening behavior cannot be modeled by conventional strain-based finite element method but can be modeled using couple stress mechanics. In this investigation, a new finite element modeling approach (FEM) based on strain field similitude is developed. The conventional displacement field was used to determine the steric rotation gradients and the additional high-order deformation energy. The mechanics basis underpinning the methodology and the conditions of applicability were detailed, and the results were benchmarked with analytical solution and experimental data. Finally, the methodology was applied to a periodic cellular structure to demonstrate the effect of steric stiffening in nanoporous solids.