The objective of this thesis is to develop and validate a computational framework based on mathematical models for the motion prediction and dynamic stability quantification of human walking, which can differentiate the dynamic stability of human walking with different mechanical properties of the leg.Firstly, a large measurement database of human walking motion was created. It contains walking measurement data of 8 subjects on 3 self-selected walking speeds, which 10 trials were recorded at each walking speed. The motion of whole-body centre of mass and the leg were calculated from the kinetic-kinematic measurement data. The fundamentals of leg property have been presented, and the parameters of leg property were extracted from the measurement data of human walking where the effects of walking speed and condition of foot-ground contact were investigated. Three different leg property definitions comprising linear axial elastic leg property, nonlinear axial elastic leg property and linear axial-tangential elastic leg property were used to extracted leg property parameters. The concept of posture-dependent leg property has been proposed, and the leg property parameters were extracted from the measurement data of human walking motion where the effects of walking speed and condition of foot-ground contact were also investigated. The compliant leg model with axial elastic property (CAE) was used for the dynamic stability analysis of human walking with linear and nonlinear axial elastic leg property. The compliant leg model with axial and tangential elastic property (CATE) was used for that with linear axial-tangential elastic leg property. The posture - dependent elastic leg model (PDE) was used for that with posture-dependent leg property. It was found that, with linear axial elastic leg property, the global stability of human walking improves with the bigger touchdown contact angle. The average leg property obtained from the measurement data of all participants allows the maximum global stability of human walking. With nonlinear axial elastic leg property, the global stability decreases with the stronger nonlinearity of leg stiffness. The incorporation of the tangential elasticity improves the global stability and shifts the stable walking velocity close to that of human walking at self-selected low speed (1.1-1.25 m/s).By the PDE model, the human walking motions were better predicted than by the CATE model. The effective range of walking prediction was enlarged to 1.12 - 1.8 m/s. However, represented by PDE model, only 1-2 walking steps can be achieved. In addition, the profiles of mechanical energies represented by the PDE model are different from that of the orbital stable walking represented by CATE model. Finally, the minimal requirements of the human walking measurements and the flexibility of simple walking models with deliberate leg property definitions allow the computational framework to be applicable in the dynamic stability analysis of the walking motion with a wide variety of mechanical property of the leg.