The mechanical properties and the electrical and thermal conductivity of composites based on an epoxy polymer (EP) filled with dispersed copper (Cu) and nickel (Ni) were studied. It was shown that the electrical conductivity of the composites demonstrated percolation behavior with the values of the percolation threshold being 9.9 and 4.0 vol.% for the EP-Cu and EP-Ni composites, respectively. Using the Lichtenecker model, the thermal conductivity of the dispersed metal phase in the composites, lambda(f), was estimated as being 35 W/mK for Cu powder and 13 W/mK for Ni powder. It was shown that introduction of the filler in EP led to a decrease in the intensity of the mechanical loss tangent (tan delta) peak that was caused by the existence of an immobilized polymer layer around the filler particles which did not contribute to mechanical losses. Using several models the thickness of this layer, Delta R, was estimated. The concept of an "excluded volume" of the polymer, V-ex, i.e. the volume of the immobilized polymer layer, which does not depend on the particle size and is determined solely by the value of the interaction parameter, B, was proposed.