There is as yet no rational basis for predicting the conditions leading to avulsion of a meandering river. Here we present a conceptual model and quantify it under simplifying assumptions as a first step toward the construction of a stability diagram for avulsion initiation. It is assumed initially that a rectangular crevasse channel of arbitrary depth is cut into the levee of a meandering river. Because the water entering the crevasse channel is derived from relatively high in the main flow, it contains low concentrations of suspended solids. Consequently, the crevasse flow is under capacity and the entrance is eroded. Deepening of the entrance increases the crevasse-channel discharge, and the concentration of suspended solids supplied, because more sediment-laden waters are tapped from the deeper flow in the main channel. The crevasse entrance is predicted to deepen until its sediment-carrying capacity is satisfied by the suspended solids entering from the main channel. Whether an avulsion will occur for a particular combination of initial conditions depends upon whether there exists steady-state hydraulic and sediment-transport conditions for crevasse channel depths that are equal to or less than the main-channel depth. This conceptual model is quantified by writing the unsteady, gradually varied, one-dimensional conservation of mass and momentum equations for water and sediment transport through a main and crevasse channel. Sediment transport is computed as the integral of a cross-sectional mean velocity and a Rouse concentration profile. Solutions show that stable crevasse channels exist only for particular combinations of the initial height of the crevasse bed relative to the water depth in the main channel and the ratio of initial crevasse bed slope to main-channel slope.