State of the art legged robots, such as the Honda’s series of bipedal robots ending in the latest advanced walking robot ASIMO, and the series of bipedal robots of Waseda University including the latest advanced robot WABIAN, employ joint-mount motors, which simplifies the analysis/design and traces the route for an effective control system, but results in legs that are heavy and bulky. Cable-driven robots overcome this shortcoming by allowing the motors to be mounted on or near the torso, thereby reducing the weight and inertia of the legs, resulting in lower overall weight and power consumption. To facilitate analysis and design, typical cable-driven robots use non-stretchable cables, which require at least n+1 motors for an n Degree-of-Freedom (DoF) joint. Therefore, for a robot with N joints, at least N additional motors are needed comparing to joint-mount motor drives. Moreover, the drive train of both joint-mount and cable-driven designs are rigid, which cannot effectively absorb ground impact shocks nor transfer potential energy to kinetic energy and vice versa when the robot is in motion, as biologic animals do. In this paper we present the design and test of a cat-size quadruped robot called RoboCat, which employs stretchable elastic cable-driven joints as inspired by biological quadruped animals. Although it complicates kinematics and dynamics analysis and design, the elastic cables allow n motors to be used for an n-DoF joint, thereby eliminating N motors for a robot with N joints comparing to non-stretchable cables, further realizing the weight and power savings of the cable driven design. Moreover, the elastic cable driven joints not only effectively absorb ground contact shock, but also effectively transfer potential and kinetic energy during walking or running, thereby improving the robot motion performance and energy efficiency. In the paper we will discuss the kinematics and dynamics analysis of elastic cable driven joints, implementation of elastic cable-driven joints on the Ohio University RoboCat, and control.