The human tongue is used in speaking, an activity unique to humans. The tongue is unusual in that it does not contain any rigid structure, such as a bone, for its muscles to act against. In an effort to better understand the biomechanics and control of the tongue, a mathematical model has been created. This model is in the form of a nonlinear controllable incompressible elastic structure that undergoes large deformations. The model was then used to solve a simplified inverse problem. The trajectories of arbitrary points within the tongue were obtained by means of tagged cine MRI. This data was then used as input to a two-dimensional simplification of the model. The output was the set of muscle activations that produced the best approximation to the observed motion in a least squares sense. This results in information relevant to two biological questions-How many independently controllable motor units are there in the tongue? How important are the dynamics of the tongue in determining its shape?.