Summary: A methodology for modeling the dynamics of a structure interacting with a fluid having a free surface is addressed. In this context, a structure is either a single-rigid container or a rigid container coupled to a flexible multibody system. All nonlinearities inherent in the dynamics of the structure are taken into account. Two models used to handle the fluid are described. The first model assumes an incompressible viscous fluid, and the second utilizes potential flow with modified Rayleigh damping. Nonlinear sloshing effects are considered, and no simplifications are made on the field equations and boundary conditions. The end result of the methodology is a set of first-order differential equations for the motion of both the structure and the fluid. Emphasis is placed on the point that the motion of the structure is not prescribed but is found as part of the solution procedure. Numerical examples and experimental results justifying the approach are presented.