Abstract An accurate description of the mechanical response of α-titanium requires consideration of mechanical anisotropy. In this work we adapt a polycrystal self-consistent model embedded in finite elements to simulate deformation of textured α-titanium under quasi-static conditions at room temperature. Monotonic tensile and compressive macroscopic stress–strain curves, electron backscattered diffraction and neutron diffraction data are used to calibrate and validate the model. We show that the model captures with great accuracy the anisotropic strain hardening and texture evolution in the material. Comparisons between predictions and experimental data allow us to elucidate the role that the different plastic deformation mechanisms play in determining microstructure and texture evolution. The polycrystal model, embedded in an implicit finite element code, is then used to simulate geometrical changes in bending experiments of α-titanium bars. These predictions, together with results of a macroscopic orthotropic elasto-plastic model that accounts for evolving anisotropy, are compared with the experiments. Both models accurately capture the experimentally observed upward shift of the neutral axis as well as the rigidity of the material response along hard-to-deform crystallographic direction.