Compliant movement and stress buffering of the torso are particularly important for state transition during high-speed locomotion in quadrupedal mammals. Currently, passive compliant control is commonly used in bionic torsos of quadruped robots, while active compliant control remains rare and immature. In previous research, we developed an active six-Degree-of-Freedom (DoF) bionic parallel torso. In this paper, we establish a muscle model that includes four biomechanical elements representing muscle characteristics (muscle force-fiber length and muscle velocity relationships) from the perspective of biology and physiology. We propose a musculoskeletal model that simulates the biological motion control system to control the compliant movement of each joint of the parallel mechanism. This model includes: 1) a neural equilibrium point controller that represents the transmission of motion commands, 2) activation dynamics that describe the activation of stimulated muscles, 3) contraction dynamics that emphasize the biomechanical characteristics of muscle tendons, 4) skeletal dynamics that describe bone movement. The effects of flexor and extensor stimulation on muscle activation, force, length, and velocity were analyzed. The results showed that both the flexor and extensor muscles will contract after corresponding stimulation. Furthermore, adjusting muscle stimulation through the musculoskeletal model can drive the parallel mechanism to reach the desired position. The musculoskeletal control method based on external force feedback can establish new torque balance in joints and drive the parallel torso to achieve compliant movements. Simulation and experiments have demonstrated the feasibility of the musculoskeletal control method. This method enhances the compliance and environmental adaptability of the parallel torso in practical applications.