Anisotropy in elastic properties of Ti-24mol%Nb-3mol%Al (TiNbAl), a new biomedical shape memory alloy developed by our group, was characterized in a temperature range from 133K to413K. A well developed < 110 >(beta){112}(beta)-type recrystallization texture is formed by an annealing at 1273K for 1.8 ks after a severe cold-rolling. Young's modulus of the beta-phase exhibited a strong anisotropy depending on the loading direction. Young's modulus along < hkl > of beta-phase of TiNbAl around room temperature was estimated to be E (< hki) (>)=(1/25 similar to 2 center dot 0.04 center dot Gamma < hkl >)(-1) GPa, with assuming that the texture is perfectly developed.