Abstract Tension induced phase transformation in pseudoelastic NiTi leads to inhomogeneous deformation with the austenitic and martensitic phases coexisting. Deformation of nearly 7% is recovered on unloading during which the deformation is again inhomogeneous. By contrast, under compression the transformation stress is significantly higher, the strain is lower and is essentially homogeneous. In pure bending experiments on pseudoelastic NiTi tubes, this asymmetry manifests as coexistence of two curvature regimes with diamond-shaped patterns of martensite developing on the tensioned side. Two curvatures exist also on unloading accompanied by progressive erasure of the diamond patterns. A recently developed constitutive model for the pseudoelastic behavior of NiTi is implemented in a finite element analysis used to simulate the tube bending experiments. The model captures the tension/compression asymmetry by incorporating both the tensile and compressive responses of the material, and includes softening over the extents of the unstable branches of the tensile response. The analysis reproduces the major features of the experimental results and provides insight into how the nonlinearities of the NiTi material interact with geometric nonlinearities to produce: the hysteretic moment-end rotation response with an upper and a lower plateau, the values of the two curvature regimes during loading and unloading, and the progressive initiation of higher strain diamond patterns on the tensioned side and the nearly homogeneous deformation on the compressive side. The sensitivity of the solution to the mesh and the softening moduli is discussed.