While the concept of visual saliency has been previously explored in the areas of mesh and image processing, saliency detection also applies to other sensory stimuli. In this paper, we explore the problem of tactile mesh saliency, where we define salient points on a virtual mesh as those that a human is more likely to grasp, press, or touch if the mesh were a real-world object. We solve the problem of taking as input a 3D mesh and computing the relative tactile saliency of every mesh vertex. Since it is difficult to manually define a tactile saliency measure, we introduce a crowdsourcing and learning framework. It is typically easy for humans to provide relative rankings of saliency between vertices rather than absolute values. We thereby collect crowdsourced data of such relative rankings and take a learning-to-rank approach. We develop a new formulation to combine deep learning and learning-to-rank methods to compute a tactile saliency measure. We demonstrate our framework with a variety of 3D meshes and various applications including material suggestion for rendering and fabrication