The École Polytechnique Fédérale de Lausanne (EPFL) has acted as official scientific advisor for the Alinghi Team, winner of the 2003 Edition of the America's Cup. In this report we discuss the role plaid by mathematical and numerical models in yacht design. In particular, several numerical simulations based on the approximate solution of the Reynolds Averaged Navier-Stokes Equations (RANS) are addressed. Numerical results in different research areas (design of appendages, free-surface flows, aerodynamics of sails) are presented and their integration in the overall design process is discussed