The population of older people in the world has grown rapidly in recent years. To alleviate the increasing burden on health systems, automated health monitoring of older people can be very economical for requesting urgent medical support when a harmful accident has been detected. One of the accidents that happens frequently to older people in a household environment is a fall, which can cause serious injuries if not handled immediately. In this paper, we propose a motion classification approach to fall detection, by integrating the techniques of motion capture and machine learning. The motion of a person is recorded with a set of inertial sensors, which provides a comprehensive and structural description of body movements, while being robust to variations in the working environment. We build a database comprising motions of both falls and normal activities. We experiment with several combinations of joint selection, feature extraction, and classification algorithms, showing that accurate fall detection can be achieved by our motion classification approach.