A nonlinear criterion of the static strength of products made of structurally heterogeneous materials, whose mechanical properties depend strongly on the reduced volume and stressed state mode, is proposed and substantiated on the basis of the generalized Pisarenko–Lebedev criterion. Based on the proposed criterion, we estimated the strength of cemented carbide components of cylindrical and recessed anvil high-pressure apparatus for the synthesis of diamonds and other superhard materials after their assembly and under operating conditions with working pressure and thermal loading. For the above loading conditions, we determined the values of reduced volume and mechanical characteristics of the cemented carbide VK6, which enter into the Pisarenko–Lebedev criterion. We study the dependence of the strength of geometrically similar components of high-pressure apparatus on their working volume.