Two variant selection criteria are often used in shape memory alloys (SMAs). One is the maximum resolved shear stress (RSS) criterion and the other is the maximum transformation work criterion. In this paper these two measures are calculated using the crystallographic theory of martensite (CTM) for the shape memory effect (SME) case and the crystallographic theory of martensite + detwinning, distortion and slip (CTM + DDS) for the superelasticity (SE) case. The results are compared with the experimental measurements of a CuAlNi single-crystal SMA. The comparisons show that work is better as a variant selection criterion than RSS. In the SME case, type-II twin variants are more favorable under uniaxial tension; while type-I twin variants are more favorable under uniaxial compression. The calculation also shows that a great tension-compression asymmetry exists in CuAlNi single crystals.