The article deals with design the road constructions by ensuring the shear resistance of the subgrade soil and pavement layers made of weakly cohesive materials. The analysis of Mohr–Coulomb plasticity criterion was performed and it was found, that in case of a limiting condition state by this criterion pavement smoothness goes out of the limits regulated by normative documents. On the basis of analysis of Drucker-–Prager yield criterion there were obtained formulas connecting ultimate strength uniaxial compression and tension with the parameters of MohrCoulomb failure envelope. Substitution of these expressions into the original criteria for the strength of materials, that are continuums, allowed modifying certain conditions so that the tensile strength changed the angle of internal friction and cohesion. A number of dependencies for calculating safe pressure on discrete material of half-space is obtained from the modified conditions of plasticity. Comparison of the numerical results to experimental data allowed determining the most suitable formula for the design of road constructions.