The objective of this paper is to study the dynamic simulation of a tether as it is deployed or retrieved by a winch on a satellite orbiting around earth. In an effort to understand the problem incrementally, the following three models were developed: (a) Model 1: A tether with constant length moves on earth in the plane of constant gravity; (b) Model 2: A tether is deployed from a drum on earth in the plane of constant gravity, i.e., length of the cable changes during deployment; (c) Model 3: A tether is deployed from a drum on an orbiting satellite. These models have been chosen to bring different aspects as well as levels of difficulty in the analysis. For example, in Model 1, the length of cable is fixed and the gravity direction is constant during motion. The equations of motion for this model are derived using Newton’s laws and Hamilton’s principle to show the equivalence of the two methods. In Model 2, free length of the cable changes during deployment. The changing length of the cable introduces coupled nonlinearities into the motion. Model 3 includes the orbital effect on the motion of deployed cable. Each of these three dynamic models characterized by partial differential equations are first converted to a finite number of ordinary differential equations using Ritz’s procedure and are then numerically integrated using Matlab ODE solvers.