The strengthening effect for a composite with nanoscale fillers is directly related to the features of interaction between the filler solid phase, the polymeric matrix, and the formed interphase layer on their contact interface. The objects of investigation were elastomeric composites on the basis of the styren butadiene matrix filled with particles of the mineral schungite. The estimation of deformation characteristics of elastomeric composite materials was carried out in the volume statement by using the developed analytical-numerical methods, which implement the analytical solutions in the form of finite series using numerical methods. The problem of determining the effective characteristics of an elastomeric composite material on the basis of styrene butadiene rubber was solved depending on the radius of inclusions with the volume schungite filling fraction of 2%.