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Recently, the theory of elasticity with surface stresses was developed for nanomechanical problems. Within this theory, the surface stresses act on the body boundary.

In our researches we extend the linear theory of elastic shells for this case. We obtained the equations of equilibrium and constitutive equations for the stress resultants and couples tensors while taking into account the surface stresses acting on the shell surfaces. The effective shell stiffness, in particular, the bending stiffness depends here also on the surface elastic moduli, which is substantial for nanodimensional thicknesses. We also consider the effective stiffness properties of the nanoporous materials like as nanofoams.