Magnesium (Mg) alloys have recently been put under the spotlight for their specific strength, the highest among structural metals. Although the mechanical behaviour of Mg alloys at quasi-static strain rates has been extensively modelled in the recent years, high strain rate studies have been much scarcer. This is mainly due to the rate dependent (RD) mechanical response of their hexagonal close-packed (hcp) crystalline structure. As a result, existing RD models do not account for the differentiated rate sensitivities of each slip and twin systems. Instead, the rate dependency is often conceived as a numerical artefact utilised to smooth the elasto-plastic transition and facilitate the scheme convergence. We thus propose a novel efficient RD crystal plasticity model for hcp metals, applied here to a rolled Mg AZ31 alloy sheet at room temperature. The constitutive RD equations are solved at each time step by either a Newton-Raphson based implicit scheme or an explicit scheme modified so as to ensure convergence independently of the stochastic bursts of slip systems inherent to such approach. Most of the model parameters are taken from the previously calibrated rate independent (RI) model of Fernandez et al. (2011), except for the new RD variables (strain rate sensitivity coefficients and reference shear strain rates), taken from the literature when available, or chosen so as to fulfill full compatibility with the RI model under quasi-static conditions. The model is validated against uniaxial compression tests at high strain rate (10(3) s(-1)), in the rolling and normal directions. The results reveal the ability of the model to simulate the mechanical behaviour of Mg AZ31 alloy under a very large range of loading rates. To the best of the knowledge of the authors, the proposed model is the first RD continuum model for hcp metals involving physically accurate slip and twin system rate sensitivities, while ensuring convergence. (C) 2016 Elsevier B.V. All rights reserved.