Using the rectilinear coordinate system the equation of continuity of mass sediment transport is derived, and the continuity equation is used to help in describing mathematically the phenomenon of scour by the continuity equation. The relationship between the shape of the scour hole and its variation with time is investigated for different conditions of scour and deposition. Expressions for distribution of sediment transport along the bed are derived for each condition. The impingement of a two-dimensional on a normal boundary is analyzed by making the assumption that the Bernoulli Equation is valid in the neighborhood of the stagnation point. Plane, potential flow is considered first, followed by flow of a fluid with viscosity. For flow with viscosity from submerged and non-submerged outlets, expressions for the horizontal velocity and shear distribution along the boundary are developed using Bernoulli's theorem and the boundary layer theory. The variation of the depth of scour is determined for two conditions of outlets by assuming a law of open channel flow for sediment transportation and by using the previously determined shear distributions and the continuity equation. In particular, the variation of scour depth with respect to time and the final depth of scour are described theoretically in terms of dimensionless parameters. It is then shown that the development of the scour hole with respect to time follows the power law and the logarithmic law for the submerged and non-submerged outlets respectively before the final state is reached. The influence of the angle of the jet is analyzed in the manner as the case of a vertical jet. In this case, expressions for the variations of the depth of scour with respect to time and the final depth of the sour are also developed.