The hydroelasticity problem related to multi-hull ship plate vibrations excited by periodic and transient surface wave forces is analyzed. Theoretical method based on the Wagner theory and empirical methods based on classification society ABS rules are considered for determining the transient slamming force on the ship hull. A boundary integral method based on the simple source distribution (Yeung ) and mixed Eulerian and Lagrangian (MEL) formulation (Longuet-Higgins and Cokelet ) for the determination of the slamming force is in progress. A suite of plate theories, ranging from small-amplitude linear undamped isotropic plate theory to damped nonlinear, stiffened-plate theories, are considered to determine the vibrations of ship-hull plates subject to the wave forces. In the present work, finitedifference algorithms are developed to solve the nonlinear plate equations. Results for range of sea states and hull scantlings are obtained to determine key structural parameters affecting the structural integrity. The algorithms and the methodology developed can be used for efficient design of multi-hull ships, and perhaps also to update classification society rules on structural design. Copyright © 2012 by ASME.