In this investigation, the elastic properties and neutrons attenuation factors for some optical glasses containing Ta2O5, SiO2, and Li2O were reported. The present glasses were also consisted of ZrO2 and Nb2O5 in very small concentrations. The glasses are chemically defined as 26.47Li2O-5.88ZrO2-(20-x)Ta2O5-xNb2O5-47.06SiO2, where, x takes the values: 0, 2.94, 5.88, and 11.77 mol%. The elastic properties of these glassy specimens were determined by employing Makishima-Mackenzie's theory (M.M.T). By using the same method, moreover, the micro-hardness and Poisson's ratio were assessed. Cross sections for slow, moderated, and fissile neutrons were computed through standard expressions and models. In addition, the influence of the partial replacement of Ta2O5 by Nb2O5 on the parameters were also analysed. The glass with the lowest Nb2O5 content presented the highest cross sections for fast, moderated, and slow neutrons. The neutron-absorption ability of included glasses declined as glass density declined and Nb2O5 molar concentration increased in the glasses. Therefore, the sample with the highest Ta2O5 content is recommended for neutron absorption applications.