Kinematic wave theory is utilized to investigate diverging overland flow which does not appear to have been previously investigated in watershed hydrology. This paper is the first in a sequel of two. It developes analytical solutions for a diverging geometry for two cases: (1) when infiltration is considered through rainfall-excess, and (2) when infiltration is treated concurrently with runoff; this gives rise to a free boundary problem. Part II discusses the application of the proposed model to natural watersheds.