We have been trying to induce a quadruped robot to walk with medium walking speed on irregular terrain based on biological concepts. We propose the essential conditions for stable dynamic walking on irregular terrain in general, and we design the mechanical system and the neural system by comparing biological concepts with those essential conditions described in physical terms. PD-controller at joints constructs the virtual spring-damper system as the visco-elasticity model of a muscle. The neural system model consists of a CPG (central pattern generator), reflexes and responses. We report our experimental results of dynamic walking on irregular terrain in outdoor environment using a self-contained quadruped robot in order to verify the effectiveness of the designed neuro-mechanical system.