<p>A new mathematical model for solving a static symmetric boundary-value problem for a layer weakened by two through holes with sliding end clamping is presented. A new method based on a system of six singular integral equations has been developed and numerically tested. As a result of a highly accurate numerical study, it was found that with a decrease in the center-to-center distance or Poisson’s ratio, the relative circumferential stress increases, and with an increase in Poisson’s ratio, the maximum relative circumferential stress shifts from the base of the layer to its depth. It is shown that for a certain combination of parameters, the effect of the existence of another hole in the layer is not observed. The corresponding dependence graphs are presented.</p>