In this paper, we present the results of modelling the formation of interphase layers (a few nm thick) with specific properties, which arise around filler nanoparticles in elastomeric nanocomposites. We use a continuum model based on the hypothesis explaining the reasons for the formation of interphase layers. This hypothesis stems from the fact that the polymer chains near the surface of filler particles have the ability to change the orientation of neighboring chains, forcing them to take such an orientation in which they themselves have to be. The proposed continuum model is applied to a two-dimensional problem for description of the formation of interphase layers in the vicinity of filler particles and in the gap between them.