This paper presents an approach for modeling nonholonomic hybrid parameter multiple body systems in order to account for the combination of rigid body dynamics and elastic motions in systems and to examine the effects of control strategies on stress development in the elastic members. The method allows for continuum bodies to be represented with the postulates associated with non-linear theories, such as Timoshenko-like beams as well as higher order plate and shell theories. The variational nature of the approach provides for the derivation of the nonlinear hybrid differential equations and the boundary conditions. Pseudo-coordinates and pseudo-speeds are used to allow for the inclusion of holonomic or nonholonomic constraints that occur among the hybrid parameter bodies, including intra-domain constraints. An applications of the methodology to a problems arising in biomechanics is presented. In this context, the methodology provides a method for relating neural control to stress development in skeletal structure. Consequently, this framework allows one to illustrate the combined effects of neural control strategies, models of muscle force inclusion, and elastic assumptions on joint trajectories and stress and strain development in the bone and tendon that arise in human movement systems.