Human beings like all organisms, are subject to a variety of diseases. Musculoskeletal diseases such as arthritis, that affect our muscles and bones, are particularly debilitating in that they considerably limit our ability to interact with our environment. The symptoms of arthritis are joint pain and loss of movement. There is deterioration of the cartilage in our articulations. The precise determination of the underlying cause of the deterioration is a challenging task. It is believed that it is caused by excessive force in the joints due to inappropriate muscle forces. Since only forces in muscles just beneath the skin can be measured, the force hypothesis remains unproven. Musculoskeletal models are essential in analysing musculoskeletal diseases because they address the lack of information on the forces involved. Such models are used to estimate muscle and joint reaction forces. Determining the key elements in a musculoskeletal model to assess its quality raises several challenges. In this thesis, a musculoskeletal model of the shoulder is presented. The model is governed by the laws of rigid-body mechanics and is similar to a model of a cable-driven mechanism. The model contains both the kinematic and dynamic aspects of the shoulder. Applying the theory of rigid body mechanics requires a certain level of rigour to ensure compatibility between the kinematic and dynamic parts of the model. Therefore, a considerable part of the thesis is devoted to presenting the details of the model's construction. The model is designed specifically for estimating muscle and joint-reaction forces in quasi-static and dynamic situations. The muscle-force estimation problem is defined as a nonlinear program and solved in this thesis using a two-step approach. In a first step, the kinematics is constructed and inverse dynamics is used to estimate the associated joint torques. In a second step, the nonlinear program is solved using null-space optimisation. An initial solution to the estimation problem is obtained by taking a pseudo-inverse of the moment-arms matrix. The solution is then corrected using the matrices null-space to satisfy the constraints. This approach redefines the estimation problem as a quadratic program and considerably reduces the time required to find a solution. Once the muscle-forces are estimated, the joint reaction forces are deduced from the dynamic model. Muscle and joint-reaction forces are compared to other results from the literature.