The transportation and control of liquid masses poses a problem of immense practical interest. Slosh forces generated by the motion of the liquid can easily interfere with the safe operation of the vehicle. The successful design and execution of such operations depends upon not only the understanding, but also the ability to predict the dynamic behavior of liquids in moving containers;The numerical simulation of liquid sloshing in moving containers is considered in this study. Numerical models are developed and applied to both two and three dimensional flows. The motion of the vehicle can be quite general, given by the superposition of several rectilinear and angular time varying accelerations. The Navier-Stokes equations are recast in a non-inertial coordinate frame which follows the motion of the container. Singularities produced by the onset of sudden motions are removed from the formulation using an asymptotic analysis. A Poisson equation is used for the pressure calculation. The position of the free surface is determined by a kinematic condition. An implicit second order accurate finite difference method is used for the solution of the governing equations;A method that simplifies the coupling of the dynamics of the liquid with those of the moving vehicle is introduced. It relies on the concept of an apparent mass for the liquid, which is formulated in a manner that measures the resistance of the liquid mass to sudden changes in the acceleration of the vehicle. It enables the solution of the solid and liquid equations based on a simple explicit, rather than an implicit, coupling scheme which significantly reduces the computational requirements;Cases of liquid sloshing in containers of rectangular, cylindrical, and spherical geometry are considered. Detailed information on the flowfield and the free surface position is given for several representative cases. Effects due to the forcing conditions, liquid viscosity, surface tension, and liquid geometry, are considered in a parametric study. Information on sloshing frequencies and damping rates is included. An excellent comparison of the present numerical result is demonstrated, where possible, with previous analytical and experimental works.