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The Navier-Stokes equation is directly solved by the finite-difference method to simulate the 2-dimensional free-surface flow field generated by a submerged hydrofoil (NACA-0012) in a uniform flow. The staggered-mesh system and a body-and boundary-fitted coordinates system are adopted in the whole domain under consideration.The non-slip condition on the wing and the exact non-linear condition on the free-surface are used as the boundary conditions. Flows under three different submergence depths are simulated with the same Froude and Reynolds numbers and attack angle.In the deepest case, the calculated wave length agrees well with the measured while the wave height is appreciably less mainly due to the difference of the Reynolds number.It needs rather long computing time for the waves to develop enough to reach a stationary condition.The results for the shallowest case where the sub-breaking is suspected to take place show a numerical breaking.The criterion for the sub-breaking is applied to the computed results.It detects the appearance of breakings in the course of computation.