Smoothedparticlehydrodynamics(SPH)isamesh-freeadaptiveLagrangianparticlemethodwithattractivefeaturesfordealingwiththefreesurfaceflow.ThispaperappliestheSPHmethodtosimulatethelarge-amplitudelateralsloshingbothwithandwithoutafloatingbody,andtheverticalparametrically-excitedsloshinginatwo-dimensionaltank.ThenumericalresultsshowthattheSPHapproachhasanobviousadvantageoverconventionalmesh-basedmethodsinhandlingnonlinearsloshingproblemssuchasviolentfluid-solidinteraction,andflowseparationandwave-breakingonthefreefluidsurface.TheSPHmethodprovidesanewalternativeandaneffectivewaytosolvethesespecialstrongnonlinearsloshingproblems.