In the present paper, based on modular modeling concept, a mathematical model for the coupled nonlinear 6-DOF motions of underwater gliders is developed, and applied to investigate the characteristics of vertical and lateral motions of an autonomous underwater glider under development at National Taiwan University. In the proposed modular model, the component forces of main hull, wings, stern vertical fin and interaction among them are included. The advantage of the present model is that the hydrodynamic coefficients of these components may be estimated using existing database or empirical formula. The longitudinal motions of the autonomous underwater glider designed at NTU are controlled by separate two buoyancy engines located fore and aft, while the lateral motions are controlled by rolling an eccentric weight. Three different configurations of main wings and stern vertical fin are investigated, and the effects of main wings location to the longitudinal motion characteristics as well as the effects of stern vertical fin location to the lateral stability are clarified through a series of simulation. As the results of the present study, a configuration of main wings and stern vertical fin for the underwater glider with two separate buoyancy engines that has most preferred performance is identified, and it has also been confirmed that the developed tool is able to be used in the preliminary design stage for developing an autonomous underwater glider. In addition, the proposed modular modeling can be easily extended to another kind of underwater vehicles, such as regular AUV.