The major process affecting the configuration and evolution of terrain is erosion by flowing water. Landscapes thus reflect the branching patterns of river and stream networks. The network patterns contain information that is characteristic of the landscape's topographic features. It is therefore possible to create an approximation to natural terrain by simulating the erosion of stream networks on an initially uneroded surface. Empirical models of stream erosion were used as a basis for the model presented here. Stream networks of various sizes and shapes are created by the model from a small number of initial parameters. The eroded surface is represented as a surface under tension, using the tension parameter to shape the profiles of valleys created by the stream networks. The model can be used to generate terrain databases for flight simulation and computer animation applications.