Abstract: Several authors had estimated the displacements per atom cross sections under different approximations and models, including most of the main gamma- and electron-material interaction processes. These previous works used numerical approximation formulas which are applicable for limited energy ranges. We proposed the Monte Carlo assisted Classical Method (MCCM), which relates the established theories about atom displacements to the electron and positron secondary fluence distributions calculated from the Monte Carlo simulation. In this study the MCCM procedure is adapted in order to estimate the displacements per atom cross sections for gamma and electron irradiation. The results obtained through this procedure are compared with previous theoretical calculations. An improvement in about 10-90% for the gamma irradiation induced dpa cross section is observed in our results on regard to the previous evaluations for the studied incident energies. On the other hand, the dpa cross section values produced by irradiation with electrons are improved by our calculations in about 5-50% when compared with the theoretical approximations. When thin samples are irradiated with electrons, more precise results are obtained through the MCCM (in about 20-70%) with respect to the previous studies. (C) 2014 Elsevier B.V. All rights reserved.