The model of soil erosion on a plane slope introduced by Hairsine and Rose (this issue) is further developed by considering rill flow. The rills are considered to be parallel and incised in a homogeneous soil mass and have sediment and water flux contributed to them orthogonally. The erosive action of water flowing down these rills is described using the concept of stream power, which is assumed to be uniformly distributed around the wetted perimeter. The apportioning of the erosion and deposition processes within a rill is then considered to be influenced by the spatial extent of a deposited layer. The theory is developed for trapezoidal rills, with triangular rills and rectangular rills as special cases. Equations describing sediment continuity are presented, and numerical and analytical solutions are described for the entrainment-limited and transport-limited situations. The experiments of Meyer and Harmon (1985) are examined using this theory, and consistency of evaluated parameters is demonstrated within this data set.