In the present paper, a 2D model of elastic solid with slightly curved boundary is considered. It is assumed that the surface elastic properties are different from the those of the bulk material. We use thermodynamic as well as surface and bulk elasticity equations, Goursat-Kolosov complex potentials, Muschelishvili representation and boundary perturbation technique to solve the problem. An evolution equation is derived that gives the amplitude change of sinusoidal relief as a function of time, undulation wavelength, residual surface stress, applied mechanical loading, surface and bulk elastic constants.