Pin-on-plate and pin-on-disk wear tests are typically used for assessing the wear behavior of a given material coupling. Such a behavior is frequently described by a wear coefficient k, which is estimated, according to the Archard’s law, as the ratio between the measured wear volume V and the product of the applied normal force F and the sliding distance s, i.e. k=V/(F s). This study demonstrates that such a relationship is correct for pin-on-plate but not for pin-on-disk, particularly for flat-ended pins. Both analytical and finite element models of the two tests were developed, considering three different distances pin-disk axis. As results, wear volumes, pressure and wear depth maps were examined and compared for the same sliding distance. Though this study is focused only on the initial transient part of the wear tests, some interesting aspects arose: i) rotational effect in pin-on-disk tests affects k estimation, especially when the pin is near to the disk axis; ii) a simple analytical function is defined to correct the wear volume estimation for pin-on-disk tests; iii) due to the different sliding distances of contact points in pin-on-disk tests, pressure redistribution occurs with higher values on the inner side (closer to disk axis); the opposite trend is observed in wear depth maps. From a computational point of view, the pin-on-disk problem, only apparently simple, required very small time increments to correctly describe the circular trajectories of points, with high computational costs. Numerical strategies are currently under investigation to extend the study to the steady state phase of both tests.