Tensile tests on commercially pure alpha-titanium show a three-stage behavior giving rise to a well on the strain dependence of the work hardening. An opposite strain rate effect on the well depth is found whether specimens are elongated along the rolling or the transverse direction. Slip lines analysis reveals an initial predominance of prismatic slip, particularly pronounced in specimens strained along the rolling direction. The relative activity of prismatic slip is then observed to decrease with the samples deformation. These results provide grounds for elaboration of an elasto-viscoplastic self-consistent model based on the translated field method and an affine linearization of the viscoplastic flow rule, and capable of explaining such peculiar work hardening behavior. The model considers crystal plasticity and deals separately with mobile dislocation density and dislocation velocity. It assumes lower strain rate sensitivity as well as higher dislocation multiplication rate for prismatic systems. Based on these assumptions, the model reproduces correctly the stress strain curves and gives sound estimates of Lankford coefficients, prismatic slip activity and textures evolution. Most importantly, the opposite effect of strain rate on the well depth with regard to the orientation of the tensile axis is qualitatively retrieved, which allows putting forward an explanation of the observed phenomena.