This chapter presents an overview of some computational methods for the analysis of problems in ship hydrodynamics. Attention is focused on the description of stabilized finite element formulations derived via a finite increment calculus (FIC) procedure. Both arbitrary Lagrangian–Eulerian (ALE) and fully Lagrangian forms are presented. Details of the treatment of the free-surface waves and the interaction between the ship structure and the sea water are given. Potential flow formulations for seakeeping analysis and calculation of the added resistance in waves are also described. Examples of application of the computational methods presented to a variety of ship hydrodynamics and related problems are given.