In this paper we consider the numerical simulations of the steady linearized potential flow around a body which moves in a liquid of finite constant depth at constant speed and distance below a free surface. Two vertical segments are introduced as the artificial boundary to limit the unbounded physical domain to a bounded computational domain. A series of approximate artificial boundary conditions at the given artificial boundary are designed by imposing the continuity of the solution and its normal derivative. Then the original problem is reduced to a problem defined in a bounded computational domain, which is solved numerically by the finite element method. The numerical examples show that our artificial boundary conditions are very effective.