In this paper, the stress distribution due to the thermal field in thin slices with hyperbolic shape is analyzed. By solving a non-homogeneous Euler equation, generalized expressions for the radial and circular stresses are calculated, where integrals of the temperature distribution occur. The temperature can be obtained from a modified Bessel equation if the ratio of thermal conductivity and transfer coefficient remains constant. Numerical results are presented in relation to the effectiveness of the rib surfaces.