The effects of horizontal stress transmission on the transient evolution of non-linear viscous bodies having aspects ratios similar to active alpine rock glaciers is investigated. This is done through a comparison between a shallow-ice model, which predicts material flux to be a local function of thickness and slope, and a finite-element model, which solves the full Stokes problem. For length-to-thickness ratios ranging from one to ten, the surface evo- lution and surface velocities calculated with these two models are markedly different. Nevertheless some other aspects of the transient evolution are quite insensitive to the different sets of simplifications on which the two flow models are based. The rate-of-advance of the snout is, for example, almost identical in both cases. Length changes of rock glaciers and alpine glaciers can, thus, be calculated accurately without accounting for the transmission of horizontal stresses.