1. On the basis of plant experiments and the solution of inverse problems of thermal conductivity we obtained heat-transfer coefficients during cooling of large shells in water and air. 2. The values obtained for the heat-transfer coefficient during cooling in air differ for the outer and inner surfaces of the shell: For the inner surface they are close to the literature data, while for the outer surface they are almost twice as high. 3. The values found for the heat-exchange coefficient during cooling in water to a temperature Tsur≥150-100° are close to the value given in [4]; at lower surface temperatures the values are close to those calculated by the convective heat-exchange formulas [7]. 4. The calculations made with the M220 computer for quenching shells 3800 mm in diameter and 2500 mm high indicate good agreement between the heat-exchange coefficient and thermophysical properties of the metal (λ and c) and the experimental data both for deep layers and points near the surface. © 1980 Plenum Publishing Corporation.