In a recent paper, analytical series methods have been developed to solve the steady quasilinear unsaturated flow equations for arbitrary two-dimensional geometry and mass flux boundary conditions. We use these analytic series methods to examine the relationships among the parameters governing infiltration and the onset of saturation. As the vehicle for this analysis we use the canonical hillslope geometry, viz. an inclined permeable region whose cross-section is a long, thin parallelogram. We find that the ‘critical’ infiltration rate (at the onset of saturation) varies monotonically with aspect ratio, wetted surface fraction and dimensionless sorptive number. However, the critical infiltration rate varies nonmonotonically with the inclination of the permeable region and attains a maximum value. For clay soils it is found that the inclination has little effect on the maximum critical infiltration rate. However, large aspect ratios or wetted fraction cause a significant reduction in the maximum, to the point where infiltration rates as low as 3 mm/year cause saturation. Sandy soils tend to be saturated but if the inclination is near horizontal a small but signficant unsaturated flow is possible.