The aim of this paper is to contribute to the characterization and modelling of the plastic behaviour of thin sheets of commercial purity (CP) α-Ti. Several loading conditions are examined: uniaxial tension/compression and simple shear tests along different orientations with respect to the rolling direction. The main goal is to precisely determine the critical shear stresses and the activated slip systems at moderate strains (up ≈45% true strain). The observed anisotropic behaviour of α-Ti is explained by the influence of the loading orientation on the activation of different families of slip systems and subsequent texture evolution. The observed behaviours (mechanical data and crystallographic textures) are compared with some predictions performed with a viscoplastic affine self-consistent model in which a dislocation-based hardening law is introduced. The experimental data involved in the identification and the validation of material parameters take into account both stress–strain responses for different loading conditions and the texture evolutions. It is shown that the model predictions in terms of macroscopic stress–strain curves, texture evolution and slip activities are in good agreement with experimental data. The predicted Lankford coefficients are however, less satisfactory. This is explained by the high sensitivity of these coefficients to small variations of texture and especially to the reduction of the sharpness of the texture. Moreover, the limits of the identification of the critical shear stresses from the sole macroscopic response are clearly highlighted. The experimental data base should be enlarged in order to reduce the number of possible scenarios (i.e. combination of activated slip systems) that describe the macroscopic response.