Considered sometimes as shape memory alloy, (26at%)Nb-Ti alloys do not present any characteristic heat emission during calorimetry measurements (DSC). The absence of phase transformation during thermal loading is confirmed by X ray diffraction (XRD). Several mechanical tests have been conducted on plate samples. The tests reveal a low Young modulus and a pseudo-elastic return of almost 2%, indicating the activation of a reversible mechanism during the mechanical unloading. Infra-red measurements show that phase transformation is responsible for this behavior, pseudo-elasticity is however partial since EBSD measurements show that twinning is also activated during strengthening. After the presentation of the different experimental results, some first results of a physical-based modeling of this material are presented.