Machine components operating in sandy environments will wear because of the abrasive interaction with sand particles. In this work, a method is derived to predict the amount of wear caused by such abrasive action, in order to improve the maintenance concept of the components. A finite element model is used to simulate various tips scratching a smooth surface. The model is verified by comparing the obtained results with a set of experiments performed earlier (M. Woldman, et al., 2013, Wear, 301(1-2), pp 76-81).