A visco-elasto-plastic constitutive model is formulated for investigating the mechanics of cortical bone tissue, accounting for an anisotropic configuration and post-elastic and time-dependent phenomena. The constitutive model is developed with reference to experimental data obtained from literature on the behaviour of cortical bone taken from multiple samples. Regarding the constitutive model, a specific procedure based on a coupled deterministic and stochastic method is applied in order to determine the values of the constitutive parameters with regard to human samples. The procedure entails processing of data deduced from mechanical tests to achieve relationships between permanent and total strain, elastic modulus and strain rate, and creep elastic modulus and time. Numerical results obtained by using a finite element model are compared with tensile experimental data on cortical bone including the post-elastic range and creep phenomena. The model shows an excellent capability to describe the tensile behaviour of the cortical bone for the specific mechanical condition analysed.