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This work encompasses numerical and experimental studies of three-dimensional (3D) sloshing problems. The two-fluid viscous flow, which is solved within a stabilized finite element context, involves liquid and gaseous phases. The free surface is captured with a level set (LS) method, including the bounded renormalization with continuous penalization technique, to avoid the well-known spreading of the marker function. Specifically, this technique is improved with a volume-preserving algorithm for long-term analyses. To verify the numerical model, the responses of free-sloshing cases are compared with analytical solutions and other results computed using a Lagrangian technique. These simulations assess the influence of considering two-dimensional (2D) and 3D analyses, as well as the effects of depth and viscosity. This work presents data obtained from a forced sloshing experiment that is specifically devoted to 3D free surface behaviour. Free surface evolution measurements are used to validate the numerical method. Moreover, the effect of the initial conditions used to promote 3D behaviour in the modelling is evaluated. [ABSTRACT FROM AUTHOR]