The aim of this paper is to examine the possibility of a simple fluid‐mechanics treatment of rapid dense granular flows. In other words, we examine whether the constitutive equation can be sought in a simple relationship between the strain‐rate and stress tensors. With this aim, we first show that an inclined channel is an appropriate device for providing rheological data. Here we provide a complete rheometrical treatment, which allows to infer the shear‐stress/shear‐rate curve (for simple shear flows) from the flow‐depth/mass‐flow‐rate curve. Experi‐ments performed with glass beads and sand grains revealed an apparent decrease in the shear stress with increasing shear rate. We then demonstrate that this result, although paradoxical, is not unphysical. Moreover, more detailed theoretical analysis shows that the main issues raised by our experiments may be overcome by ‘microstructural’ models. We finally give two examples of models including a single microstructural parameter, which are able to qualitatively account for the main features of our experiments.