Flows with predominate flow direction are governed by the de Saint Venant flow equations. The kinematic wave approach retains the mass balance but considers pseudo-uniform flow conditions instead of the full momentum balance. This approximation is particularly well-suited for overland runoff processes. The zero-inertia approach may be regarded as an intermediate formulation which retains the effect of surface slope but neglects dynamical flow properties. This investigation considers in detail the differences between the three of the aforementioned approaches under pseudo-steady flow conditions. The result indicates application limits of the two simplified wave theories when compared to the de Saint Venant flow equations and may be regarded as a useful decisive criterion.