[en] The stress-strained state of an outer chamber i.e. one of the main elements of fusion reactors is studied. The problem is solved by the asymptotic methods of the elasticity theory using the regularization methods of divergent integrals. Based on the solution of this problem a formula is derived describing radial motion in a smooth torus under pressure, and a simple algorithm is constructed for studying the stress-strained state of a double torus-like shell fastened with stiffness ribs. Numerical results for the chamber with the T-20 device geometrical parameters are given. The analysis of the numerical results permits to make the following conclusions: 1. Meridional stresses reach their highest value in the maximum approach points to the torus rotation axis. Circuit stresses in these points have the minimum values. From the point of view of the strength theory it is favourable, because equivalent stresses appear to be distributed relatively uniformly. 2. In the points of fastening of stiffness ribs sufficient increase of local stresses is observed. These stresses are higher on the inner torus than on the outer one, whereas the main stresses on the inner torus less than on the outer one. That also leads to the leveling of the general stressed state. 3. In the whole, stiffness rings increase the constructiion supporting power and, in particular, increase its stability