The viscoplastic behaviour of two batches of commercially pure titanium with different oxygen contents was characterized at room temperature through tension, creep, relaxation, and strain rate jumps tests along the rolling and transverse directions. Depending on the applied stress, creep saturated, or the primary creep stage was followed by secondary and even tertiary creep leading to fracture within a few hours. 33 to 40% of the flow stress was relaxed within 20 hours. The strain rate sensitivity was found to increase with the oxygen content and when the strain-rate-decreased. It was up to 25% higher along the transverse direction than along the rolling direction. The experimental data were used to identify a simple mean field crystal viscoplasticity model. Assuming different viscosities on prismatic and non prismatic slip systems, the anisotropy and strain rate dependence of the strain rate sensitivity were captured. As a consequence of these different viscosities, the relative contributions of each type of slip system to the overall deformation are predicted to vary with the strain rate, in accordance with some data from the literature.