The linear homeomorphic muscle model proposed by Enderle and coworkers for the rectus eye muscle is fitted to reflect the dynamics of muscles in the head-neck complex, specifically in muscles involved in gaze shifts. This parameterization of the model for different muscles in the neck region will serve to drive a 3D dynamic computer model for the movement of the head-neck complex, including bony structures and soft tissues, and aimed to study the neural control of the complex during fast eye and head movements such as saccades and gaze shifts. Parameter values for the different muscles in the neck region were obtained by optimization using simulated annealing. These linear homeomorphic muscle models provide non-linear force-velocity profiles and linear length tension profiles, which are in agreement with results from the more complex Virtual Muscle model, which is based on Zajac's non-linear muscle model.