Surface elasticity models including the Gurtin–Murdoch theory within the framework of continuum
mechanics are analyzed and applied to the 2-D boundary value problem of a circular cylindrical nanopore being
in an elastic body under remote loading. A brief overview of these models and their various applications is
provided in the paper. Assuming that the surface of the nanopore is free from an external load and incorporating
surface stresses, the general boundary equation is formulated in terms of the unknown complex displacement.
It is shown that the boundary equation of each model is a particular case of the general one. The solution of
the problem in the general case including all models leads to the singular integro-differential equation which is explicitly evaluated. The final solution is presented for the stress field by means of elementary functions. The effect of each model on the stress field arising around the nanopore due to uniaxial remote loading is numerically investigated. It is disclosed that some models display both the great deviations and qualitative differences from the Gurtin–Murdoch model.