Aiming at the problem that the traditional biped robot model lacks the feet mass and the torso， a flexible biped robot model considering the influence of swing leg dynamics and torso was proposed， and its walking control and stability were studied. Firstly， the dynamics model of the system was established and the dynamics equation was deduced by the Euler-Lagrange method. At the same time， based on the Spring-Loaded Inverted Pendulum （SLIP） model， by adding rigid torso， foot mass， and adopting telescopic legs of variable length， the influence of the torso and the dynamics of swing legs on the gait of the robot was fully considered. Then， the feedback linearization controller based on variable length legs was designed to track the target trajectory and regulate the attitudes of the swing legs and the torso. Finally， the Newton-Raphson iteration method and Poincaré map were adopted to analyze the fixed point and orbital stability conditions of the robot. Simulation analysis was carried out based on theoretical analysis. Simulation results show that the proposed controller can realize the robot’s periodic walking and has good robustness to the external interference. And the moduli of all eigenvalues of the Jacobian matrix are less than 1， forming a stable limit cycle， which proves that the system has orbital stability.