The main objective was to developconcepts of the mechanics of gully bank failures, specifically, the effect of groundwater on soil shear strength and the interaction with gravitational forces on the soil. The concepts were expressed as digital computer programs that evalutate gully bank stability. Two groundwater flow systems defined as boundary value problems were solved for the hydraulic potential function by a modified Gram-Schmidt technique. One model can be used to evaluate effects of seepage recharge on groundwater flow into the gully. The second was used to analyze the effects of water table fluctuations in the vicinity of the gully bank, notably cases of rapid drawdown. The solutions apply to gullies with sloping banks which are seepage faces for groundwater. (Modified author abstract)