A mathematical model of the stream flow in border irrigation is presented in the context of negligible accelerations everywhere in the stream. During the advance phase, numerical solution of the governing equations is achieved on an oblique grid in the x-t plane. The equations of motion are integrated over each oblique cell formed by joining the node points at constant times and distances by diagonals. The resulting nonlinear algebraic equations for depth and discharge at the upper corners of a cell (on the unknown time lines) are linearized with respect to the known values at the lower corners. The resultant set of linear algebraic equations in the incremental changes of depth and discharge that occur over the time interval are solved by a double-sweep technique. During runoff and recession, the grid is changed to a rectangular net. Solutions for advance recession and runoff volume compare very favorably with the results of models based on the complete hydrodynamic equations and with field tests, at but a fraction of the expense.