Beam and Warming implicit Unite difference schemes are introduced to integrate the equations describing the two-dimensional unsteady free-surface flows. These schemes are second-order accurate in space and time, allow sharp discontinuous initial conditions, and do not require isolation of a bore. Subcritical and supercritical flows may be present indifferent parts of the channel or they may occur in sequence. Depending upon the Courant number used in the computations, sharp discontinuities may be slightly smeared since they are not isolated. Different procedures for incorporating the boundary conditions are discussed. The analysis of two-dimensional unsteady free-surface (lows resulting from the breaking of a dam are presented to illustrate the aplication of the methods.