A 3D finite-strain constitutive model for shape memory alloys (SMAs) is proposed. The model can efficiently describe reversible phase transformation from austenite to self-accommodated and/or oriented martensite, (re)orientation of martensite variants, minor loops, latent heat effects, and tension–compression asymmetry based on the Eulerian logarithmic strain and the corotational logarithmic objective rate. It further accounts for transformation volume contraction, smooth thermomechanical response, temperature dependence of the critical force required for (re)orientation, temperature and load dependence of the hysteresis width, asymmetry between forward and reverse phase transformation, and is flexible enough to address the deformation response in the concurrent presence of several phases, i.e., when austenite, self-accommodated and oriented martensite co-exist in the microstructure. The ability of the proposed model to describe the aforementioned deformation response characteristics of SMAs under multiaxial, thermomechanical, nonproportional loading relies on the set of three independent internal variables, i.e., the average volume fraction of martensite variants, their preferred direction, and the magnitude of the induced inelastic strain, that further allow for an implicit description of a fourth internal variable, the volume fraction of oriented as opposed to self-accommodated martensite. The calibration of the model and its numerical implementation in an efficient scheme are presented. The model is validated against experimental results associated with complex thermomechanical paths, including tension/compression/torsion experiments and the efficiency of its numerical implementation is verified with simulations of the response of a biomedical superelastic SMA stent and an SMA spring actuator.