A revision is made of Labusch’s simplified solution for the statistical problem of estimating the critical resolved shear stress for a dislocation moving through a random array of solute-based pinning points. The classical old solution predicts that the critical resolved shear stress contribution from atoms in solid solution, scales with of the binding energy between a straight dislocation and a solute atom, in the power of 4/3, and with the concentration of solute atoms in the power of 2/3. This estimate is important and commonly used in multiscale simulations, from which refined binding energies of straight dislocation segments can be estimated from atomistic simulations. In the current work, a precise numerical solution of Labusch’s model is found, based on discrete dislocation dynamics simulations of a dislocation gliding through an array of elastic stress fields from a high number of randomly distributed solute atoms above/below the slip plane. A revision of the scaling relations between the critical resolved shear stress and the solute concentration is reported.