We propose a mechanical model of eyeball movements based on a parallel kinematics mechanism, where the extraocular muscles can be replaced by cables.Based on this framework, we present the anatomical conditions for the eyeball movement, analyze its inverse kinematics to obtain isodeformation curves of extraocular muscles.A computer application was developed that simulates eyeball movement and displays the associated deformation curves in real time.The results are a novel contribution to the modeling of biomechanical systems using kinematics theory; the computer application is a useful resource for medical and clinical training.