A path on a polygonal terrain is gentle if it does not ascend or descend too steeply, i.e., its gradient is below a given threshold θ at every point. The constriction to gentle paths makes the shortest path problem more realistic as vehicles usually can not traverse arbitrarily steep slopes. We give a (1 + ε)-approximation algorithm for the shortest gentle path problem. The running time lies in O ( n5.5 log nε ) where n denotes the number of vertices of the terrain and is thus independent of the geometry of the terrain. Furthermore we discuss the open question whether the shortest gentle path problem is NP-hard and since we could not prove hardness develop ideas for an exact algorithm.