This paper studies the cyclical dynamics of skill mismatch and quantifies its impacton labor productivity. We build a tractable directed search model, in which workersdiffer in skills along multiple dimensions and sort into jobs with heterogeneous skill requirements. Skill mismatch arises due to information frictions and is prolonged by search frictions. Estimated to the U.S., the model replicates salient business cycle properties of mismatch. Job transitions in and out of bottom job rungs, combined with career mobility, are key to account for the empirical fit. The model provides a novel narrative for the scarring effect of unemployment.