Legged robots are highly attractive for military purposes such as carrying heavy loads on uneven terrain for long durations because of the higher mobility they give on rough terrain compared to wheeled vehicles/robots. Existing state-of-the-art quadruped robots developed by Boston Dynamics such as LittleDog and BigDog do not have flexible bodies. It can be easily seen that the agility of quadruped animals such as dogs, cats, and deer etc. depend to a large extent on their ability to flex their bodies. However, simulation study on step climbing in 3D terrain quadruped robot locomotion with flexible body has not been reported in literature. This paper aims to study the effect of body flexibility on stability and energy efficiency in walking mode, trot mode and running (bounding) mode on step climbing.