In this paper we develop analytical solutions for scratch hardness–strength relations for cohesive-frictional materials of the Mohr–Coulomb and Drucker–Prager type. Based on the lower bound yield design approach, closed-form solutions are derived for frictionless scratch devices, and validated against computational upper bound and elastoplastic finite element solutions. The influence of friction at the blade–material interface is also investigated, for which a simple computational optimization is proposed. Illustrated for scratch tests on cement paste, we show that the proposed solutions provide a convenient way to determine estimates of cohesion and friction parameters from scratch data, and may serve as a benchmark to identify the relevance of strength models for scratch test analysis. Copyright © 2011 John Wiley & Sons, Ltd.