A model for the collision between a sand grain and a body of yardang material is established by using the principles of classical mechanics. A new nondimensional parameter, the "abrasion number" A(n), is derived from the model. The volume removed per impact for different targets is proportional to A(n) approximately. As an indicator of the energy ratio of the impacting material to the target material, A(n) not only reflects the previous "abrasion law" but also introduces two dominant mechanical parameters, Young's modulus and yield stress. We propose A(n) to be a similarity criterion for abrasion experiments. The practicability of the model under natural conditions is examined by an example. It is concluded that the abrasion rates of yardangs in the western Qaidam basin, China, are 0.011-0.398 mm/yr in the period of 1986 to 2010 and remarkable abrasion events generally correspond with strong wind conditions. The model will be helpful for reconstructing the history of aeolian activities from the morphologies of yardangs in the arid regions on Mars.