The objective of this study was the modification of a linear homeomorphic horizontal saccadic eye movement model to a direct programming state-space representation through Laplace variable analysis about the operating point or initial eye position. The lateral and medial rectus muscle of each eye is modeled as a parallel combination of an active state tension generator with a viscosity and elastic element, connected to a series elastic element. The eyeball is modeled as a sphere connected to a viscosity and elastic element. Each of these elements is assumed to be ideal and linear.