In the design of roads, a number of engineering tasks that requires determining the stress state of the road structure are solved: estimating the stability of the embankment, calculating the load resistance, predicting deformations, determining the loads affecting on the culverts and communication lines in the body of the roadbed, etc. The solution of these tasks in the design of ash and slag mixture embankments cannot be performed due to the insufficient knowledge of the stress state formation mechanisms in similar solids. The article reviews and compares theoretical solutions for predicting stresses in a continuous and granular environment arising in the body under the flat plate effect on its surface. The tests were carried out on a solid with a compaction coefficient (0.95), with five values of humidity (from 22 to 38 % by weight). The results of experimental studies on the change in pressure arising in the ASM at different depths, when exposed to the vertical load from the stamp, are presented. The value of the shear resistance to increase by 21 % with an increase in moisture content from 22 % to 28 %, and with further growth returned to almost the original values without any visible effect on the stress distribution. Conclusions about the insignificant effect of humidity on the stress distribution in the ASM were drawn (at least under the chosen experimental conditions). Estimates of mathematical models for stress prediction in relation to the bulk body from the ash and slag mixture are given. To determine the distribution environment coefficient in the Fröhlich model, a correlation dependence between the CBR and the modulus of elasticity was derived. This correlation allowed us to link the theoretical solutions of Gonzalez and earlier experiments on the evaluation of the modulus of elasticity of embankments from ASM at different humidity with the stresses distribution.