Recently, robots are expected to support our daily lives in real environments. In such environments, however, there are a lot of obstacles and the motion of the robot is affected by them. In this research, we develop a musculoskeletal robotic arm and a system identification method for coping with external forces while learning the dynamics of complicated situations, based on Gaussian process regression (GPR). The musculoskeletal robot has the ability to cope with external forces by utilizing a bio-inspired mechanism. GPR is an easy-to-implement method, but can handle complicated prediction tasks. The experimental results show that the behavior of the robot while interacting with its surroundings can be predicted by our method.