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This paper describes fully nonlinear two-dimensional numerical calculations of the free-surface deformations of initially calm water caused by the forced motion of totally or partially submerged horizontal circular cylinders. The paper considers the following.(i) Totally submerged cylinders moving with constant velocity in vertical, horizontal or combined motions. Results are compared with the small-time asymptotic solution obtained by Tyvand & Miloh in 1995. Their results, which are taken to third-order (which is when gravity terms first appear in the expansions), are in excellent agreement with the numerical calculations for small times; beyond this only the numerical method gives accurate results until the free surface breaks or the cylinder emerges from the free surface. Breaking can occur during exit due to strongly negative pressures arising on the cylinder surface, or during the downwards motion causing a free-surface depression which closes up rapidly, forming splashes. Downwards motion is also shown to give rise to high-frequency waves in some cases.(ii) The free-surface deformations, pressures and forces acting on a cylinder in vertical or oblique forced motion during engulfment when it submerges from being initially half-submerged. The initial stages, when the cylinder still pierces the free surface, specify the initial conditions for a separate program for a completely submerged body, thereby allowing complete engulfment to be studied. The free surface closes up violently over the top of the cylinder resulting in jet flow, which, while difficult to handle numerically, has been shown to be insignificant for the bulk flow and the cylinder pressures and forces.

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