The mathematical description of nonlocal interactions of particles of the continuum has a number of features. It is of practical importance to take into account those features that make it possible in principle to simultaneously describe in the local (weakly local) approximation two effects observed in elastic materials - the appearance of a boundary layer in the vicinity of the free surface and the nonlinearity of the dispersion law of high- frequency acoustic waves. These effects are explainable from the point of view of solid state physics, which takes into account the discrete atomic structure and interatomic potential interactions occurring at finite distances, but within theframework of one model they are not considered in the mechanics of continuous media. This paper shows the fundamental possibility of implementing such a description within the framework of one model.