The Ti-Nb-Fe-Cr alloys are used in various fields, such as nuclear radiation shielding, cladding material in nuclear reactors, and implants in the medical field. It is one of the best materials for biomedical applications as it is biocompatible, is corrosion resistant, and has good mechanical properties. As nuclear radiation emanates from various sources in a nuclear reactor, the behavior of this alloy with the interaction of gamma and neutrons has not been well studied. In the present investigations, the interaction of gammas and neutrons with Ti-27Nb-7Fe-xCr (x = 0, 2, 4, 6, and 8 wt%) alloys is studied in order to understand the radiation shielding properties and their usefulness in biomedical applications. Gamma-ray–interaction parameters such as MAC, HVL, MFP, Zeff, Zeq, Neff, and multilayer energy absorption buildup factor (MLEABF) are estimated using EpiXs, PyMLBUF, and NGCal software in the energy range of 1 keV to 15 MeV. The multilayer buildup factor (MLBF) is calculated for cortical bone and for alloys with varying Cr concentrations. Comparison of the MLBF values of alloys with cortical bone shows that in the lower-energy region as well as the higher-energy region above 0.5 MeV, alloys and cortical bone yield the same values, indicating that the alloys behave as cortical bone in this energy region. Mass attenuation factors (MAFs) of thermal and fast neutrons are also calculated for various elastic modulus values of selected alloys at thermal and fast neutrons. It is found that the elastic modulus increases with increasing MAF values of both fast and thermal neutrons. By increasing the Cr content in the Ti-27Nb-7Fe alloy, the elastic modulus decreases. The relationship between the MAF of neutrons and the elastic modulus of the alloy is established for the first time.