In biomechanics and robotics, elasticity plays a crucial role in enhancing locomotion efficiency and stability. Traditional approaches in legged robots often employ series elastic actuators (SEA) with discrete rigid components, which, while effective, add weight and complexity. This paper presents an innovative alternative by integrating continuously compliant structures into the lower legs of a bipedal robot, fundamentally transforming the SEA concept. Our approach replaces traditional rigid segments with lightweight, deformable materials, reducing overall mass and simplifying the actuation design. This novel design introduces unique challenges in modeling, sensing, and control, due to the infinite dimensionality of continuously compliant elements. We address these challenges through effective approximations and control strategies. The paper details the design and modeling of the compliant leg structure, presents low-level force and kinematics controllers, and introduces a high-level posture controller with a gait scheduler. Experimental results demonstrate successful bipedal walking using this new design.