Photonuclear reactions play an important role in many different subfields of nuclear astrophysics, and fields, such as nucleosynthesis applications. The photonuclear reaction cross sections, especially the photoneutron reaction cross sections, are the fundamental properties of nuclear systems. In this study, theoretical evaluation of photoneutron reaction cross sections for 2 7 <= A <= 2 3 8 targets (Al-27, Mo-96, Ta-181, U-238) have been investigated in the incident photon energy range of 7-35 MeV. Monte Carlo code TALYS 1.6 was used to calculate the photoneutron cross sections. The results are compared with the earlier experimental reports in literature and the cross section data in the TENDL-2013 nuclear reaction data library, based on subsequent versions of the TALYS nuclear code system. The photoneutron cross section results and the effects of the mass number of target nuclei are discussed.