This dissertation presents a constrained multi-body dynamics method to study musculoskeletal disorders due to human vibration. The method uses Kanes equations to develop governing equations of a multi-body human-body model subjected to constraints. Kanes equations are modified to accommodate the constraint forces. It is observed that the resulting generalized constraint force array is proportional to the transpose of the matrix of coefficients of the constraint equations. This theoretical method is used to obtain a computational simulation of a heavy equipment operator subjected to whole body vibration due to multiple shocks in a working environment. The objective of this study is to determine the mechanism of shock inducing low back pain and disorder. To this end we develop a quantitative relation between vibration excitation and human response. The simulation model consists of a 17-segment system of bodies representing the bodies of the human frame. The bodies are connected by springs and dampers simulating the human joints. The model is validated by comparing computed head transmissibility response with experimental recorded data. The dissertation discusses a multi-body sitting human body model subjected to lower amplitude and high amplitude acceleration exposures containing multiple shocks. The simulation results are compared to published data. The dissertation presents a vibration analysis procedure to conduct time domain and frequency domain human body dynamics. Finally, the dissertation presents a means of predicting health risk under different vibration environments.