This paper investigates the dynamics of an underwater vehicle-manipulator system (UVMS) consisting of a two-link flexible-joint manipulator affixed to an autonomous underwater vehicle. The quasi-Lagrange formulation is utilized in deriving a realistic mathematical model of the UVMS considering joints’ friction, hysteretic coupling between the joints and links, and the nonlinear hydrodynamic forces acting on the system, such as added mass, viscous damping, buoyancy, drag, and vortex-induced forces. Numerical simulations are performed to demonstrate the effects of hydrodynamic forces and system coupling between the vehicle and the manipulator and the joints and the links on the precise positioning of the end effector.