In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of Szekeres class I and II metrics, we consider the Einstein, Bergmann-Thomson and Landau-Lifshitz energy definitions in the teleparallel gravity (the tetrad theory of gravitation (TG)). We have found that Einstein and Bergmann-Thomson energy distributions give the same results, Landau-Lifshitz distribution is disagree in TG with these definitions. These results are the same as a previous works of Aygun et al., they investigated the same problem by using Einstein, Bergmann-Thomson, Landau-Lifshitz (LL) and Moller energy-momentum complexes in GR. However, both GR and TG are equivalent theories that is the energy densities are the same using different energy-momentum complexes in both theories. Also, our results are support the Cooperstock's hypothesis.