1. The effect of three-dimensionality of the site on the distribution of stressesσy above the tunnels is considerable; the narrower the site, the greater this effect. 2. A deficit of the values ofσy relative toγsy is noted in all stages of constructing the dam. 3. The maximum stressesσy above the tunnels are reached in the middle sections of the tunnels and are slightly less thanγsy, which can be considered equal to the latter. 4. Near the tunnel walls are noted zones having a practically zero value, which is an important factor that must be taken into account when calculating the strength of the tunnels. 5. The levels of stressesσy near the canyon walls considerably lag behindγsy, which applies to all construction stages. On the basis of calculating the SSS of the dam in a three-dimensional rheological formulation, we can propose a stepped scheme of the acting vertical loads, which leads to a saving of tunnel concrete.