The influence of various types of fillers – graphite nanoplatelets (GNPs), multi-walled carbon nanotubes (CNTs) and additional boron nitride (BN) – on the mechanical properties of epoxy resins (ED20 and SEDM2) has been investigated. The content of carbon nanofiller in such composite materials (CMs) varies from 3 to 10 wt.%, while the content of BN was 27 wt.%. The mechanical properties were investigated by the uniaxial compression of cylindrical specimens of CMs. It was found that the values of elastic and plastic deformation, elastic modulus and compression strength depend on the type of epoxy resin, content of carbon filler and availability of BN in CM. Namely, the insertion of carbon fillers into the polymer matrix increases the plastic deformation of CMs, and the addition of BN increases the elastic properties of CMs. It was also shown that the compression of CM specimens leads to a significant decrease of the electrical resistance which is explained by the decrease of the contact resistance between carbon filler particles in conductive chains.