In this paper, it is demonstrated that, with the distribution of lowestorder concentrated (discrete) singularities of delta function nature, the solution to the linear free surface problem can be obtaianed with a remarkable degree of accuracy. The linearized bounday valve problem is formulated subject to boundary conditions for the determination of strengths of singularities; the simple sources above (not on) the free surface and the vortices on the body surface. Three sample calculations were performed; the flow about a submerged vortex of known strength, the flow past a submerged circular cylinder, and the flow around a hydrofoil section. The convergence of the numerical procedure is achieved with a relatively small number of elements, The final results are compared with those of the publi¬shed works, and are considered very satisfactory.