In daily life, certain textures and materials invite our touch motions. To seek the nature of such haptic invitation, we conducted a series of experiments consisting of sensory evaluations and ranking tasks for 36 materials to ascertain their perceptual properties and their degrees of haptic invitation. In addition, we recorded the human touch motions elicited by these materials. The results showed high degrees of haptic invitation for materials with perceptually prominent textures, which indicates that such textures frequently invite human touch motions. We also developed a Bayesian network model that represented the probabilistic relationships between invited touch motions and the properties of textures. The model substantiated the observation that different types of textural prominence led to different types of invited touch motions. These results collectively suggest that materials with prominent textures frequently encourage humans to touch them, using appropriate or specified touch motions.