The purpose of this study is to control the position of an underactuated underwater vehicle manipulator system (U-UVMS). It is possible to control the end-effector using a regular 6-DOF manipulator despite the undesired displacements of the underactuated vehicle within a certain range. However, in this study an 8-DOF redundant manipulator is used in order to increase the positioning accuracy of the end-effector. The redundancy is resolved according to the criterion of minimal vehicle and joint motions. The underactuated underwater vehicle redundant manipulator system is modeled including the hydrodynamic forces for the manipulator in addition to those for the autonomous underwater vehicle (AUV). The shadowing effects of the bodies on each other are also taken into account when computing the hydrodynamic forces. The Newton-Euler formulation is used to derive the system equations of motion including the thruster dynamics. In order to establish the endeffector trajectory tracking control of the system, an inverse dynamics control law is formulated. The effectiveness of the control law even in the presence of parameter uncertainties and disturbing ocean currents is illustrated by simulations.