A mathematical model of two-dimensional unsteady flow through a breached dam is developed. The numerical method of characteristics in three independent variables is used to construct an algorithm correct to second order with respect to time. The solution progresses at specified time intervals. At any time, the flow conditions are obtained by extending characteristic conoids back to a previously computed time plane and allowing information to propagate along the curvilinear rays of these conoids. Both the negative wave propagating into the reservoir and the jet emerging from the breach and eventually inundating the valley downstream of the dam are modeled in detail. Arbitrary dam geometry and channel topography can be taken into account. Propagation of the wave fronts is simulated by a computational grid moving with time. The exact computed results of the model are presented graphically as axonometric projects for the depth, and as plan-view, two-dimensional vector fields for the flow velocities.