This paper introduces a mechanistic approach to relate the sensations of touch by epithelial surfaces of for example skin, eye or mouth to the material properties of the substrate. The approach is to model the hydrodynamic and frictional forces exerted by the substrate onto the surfaces, which are deformable and compliant to these forces. Subsequently these forces are related to the neurological responses of the mechanoreceptors buried in these surfaces. The potential of the approach is illustrated for textural perception of food materials in the mouth. It leads to several concepts for textural perception in the mouth, some of which have been demonstrated previously and some of which are new. As a first example, the branching into high and low viscosity regimes for thickness perception found experimentally can be linked directly to the detection limit of the neural receptors. As a second example, by taking into account the intrinsic roughness and deformability of the papilla surface, estimates are obtained for the cross-over between the hydrodynamic friction regime, where the papilla tips are lubricated by a thin liquid film (smooth mouthfeel), and the boundary friction regime, where the papilla tips are in direct contact with the opposing surface of the palate (rough mouthfeel). This has implications for the role of viscosity on smoothness and astringency sensations. As a final example, the model suggests that the sensation of hard particles (grittiness) can be suppressed by increasing the viscosity of the medium, which is in agreement with experimental findings from sensory studies.