Pole tip recession (PTR), which is caused by differences in wear resistance of the various phases in magnetic disk and tape heads, must be reduced because it is probably the main impediment to reduction of spacing. Here, a numerical model of PTR is presented. Experimental results suggest that three-body abrasion, which leads to primarily plastic wear, is the mode responsible for PTR. In the model, the authors assume this wear mode, and assume that wear is a function of load, sliding distance, hardness of the worn surface, and dimensionless wear coefficients. As sliding proceeds, PTR increases continuously, which leads to a continuous change in contact between three-body abrasives and poles; the load carried by the poles decreases as PTR increases. This is modeled by assuming that asperities of the head and medium deform and wear plastically to accommodate passage of particles through the interface. The pole wears less as PTR increases since the opening for sliding particles increases. This accounts for the decreasing rate of change of PTR with sliding distance found for disk and tape heads numerically and experimentally. For tape heads, the model predicts that each of the following leads to higher PTR: increasing the thickness of three-body particles, increasing tape tension, decreasing pole hardness, and increasing the pole wear coefficient.