The basic formulae for the calculation of the negative thermal impulse due to the shrinkage of a circumferential weld are given as a function of welding parameters. A differential equation for the radial shell deformation is derived using the bending theory of cylindrical shells. The solution of this equation gives an approximate formula for the maximum radial deformation. Comparing this formula with the limiting deformation given by ECCS allows calculating the required shell thickness. Another thickness can be obtained using ECCS buckling formulae. Using an interpolation, a thickness can be calculated, which fulfils both constraints. Numerical examples illustrate the thickness design.