This paper deals with the effect of crystal orientation on the B19’-martensite reorientation stress and yield stress in compression in TiNi single crystals with different Ni contents varying from 50.4 to 51.2 at.%. It was experimentally shown that the martensite yield stress appears to be higher for the [111]B2-oriented single crystals than for the [001]B2-oriented single crystals regardless of Ni content. The difference between martensite yield stress for the two investigated orientations increases with the growth of Ni content. The maximum difference between martensite yield stress σcrM for two investigated orientations is 996 MPa at Ni content of 51.2 at.% (σcrM = 1023 MPa for the [001]B2-orientation and σcrM = 2019 MPa for the [111]B2-orientation). As a result of comparison with the B2-austenite yield stress, it was found that this is not an ordinary case. The [001]B2 orientation is a high-strength in B2-austenite and a low-strength in B19’-martensite. It was experimentally shown that the B19’-martensite reorientation stresses weakly depend on the orientation and chemical composition compared with the martensite yield stress. The reasons for the orientation dependence of the martensite yield stress in compression and the deformation mechanisms of B19’-martensite are discussed.