The three-dimensional axisymmetric elastic boundary value problem of the torus of a closed hollow circular cross section with varied thickness under uniform internal pressure is analyzed by the indirect fictitious boundary integral method. The configuration parameters are the radius of the torus, the mean meridional radius of the hollow circular cross section, the thickness, and the eccentricity between the outer and the inner circles of the cross section. Moreover, the leveling of the stresses in the hollow torus is investigated.