A numerical method which extends traditional one-dimensional characteristic methods for wave propagation to two-dimensional flow is presented for computing dam-break waves. In this method wave interactions and reflections in two dimensions are handled such that complex channel geometries can be easily analyzed. Stability requirements are less stringent than that for explicit finite difference schemes, and body-fitted coordinates are not needed to simulate flow through arbitrary geometries. The computed results compare satisfactorily with experimental data for dam-break flows in a straight channel and along the outer bank of a 180 degree bend.