Self-cleansing is a design criterion that satisfies a condition to keep a channel bottom clean from sediment deposits. Deposition of sediment significantly affects on the hydraulic capacity of the channel, and therefore additional costs arise for cleaning the channel. Self-cleansing models in literature are mostly developed for circular channels, which make the limited applicability of existing models. In this study, using experimental data of different cross-section channels, a self-cleansing model is suggested for computation of non-deposition particle Froude number. Considering open channel flow resistance, and using simple channel geometry parameters, a channel cross-section shape factor is incorporated into the model to make it applicable for any arbitrary channel cross-section shape. The robustness of the model is evaluated on different cross-section experimental data to show the applicability of the model on a variety of channel cross-section.