The conductivity and percolation concentration of the composite material filled with randomly distributed carbon nanotubes were simulated as a function of the mechanical deformation. Nanotubes were modelled as the hard-core ellipsoids of revolution with high aspect ratio. The evident anisotropy was observed in the percolation threshold and conductivity. The minimal mean values of the percolation of 4.6 vol. % and maximal conductivity of 0.74 S/m were found for the isotropic composite. Being slightly aligned, the composite demonstrates lower percolation concentration and conductivity along the orientation of the nanotubes compared to the perpendicular arrangement.