This book is dedicated to students, researchers, and practicing engineers in the fluid community who are faced with the challenges of extending the uses of the behavior of liquid dynamics to new frontiers of human civilization. This book provides more comprehensive knowledge on meshless local Petrov-Galerkin method, including the introduction of moving least-squares approximation with linear basis as well as Gaussian type weight functions. This book discusses the behavior of a liquid-filled container due to fluid-structure interaction effects. The highlights are: slosh frequency, slosh displacement, free surface profiles, hydrodynamic pressure developed on container walls, coupled effect of sloshing and the container responses due to change in the liquid pressure. This book also introduces an experimental study to have an insight into some basic aspects of the sloshing phenomenon.