The boundary value problem of thermomechanics for non-uniform alloyed vitrifying cylindrical rod has been developed. The step-iterative finite element solution algorithm of this problem is presented. On the basis of the developed numerical model regularity of formation technological and residual stresses in the non-uniform alloyed quartz rods at cooling and the subsequent removal of external layers are researched. Dependence of concentration of an alloying substance on radius of the rod, admissible from the point of view of strength is established.