Although we have had the problem of dynamic thermal stress distribution solved in the surface of a cavity in some special shapes, a general solution to this problem for an arbitrary-shaped cavity was still not obtained. Using the complex function method, the paper analyzed the dynamic thermal stress distribution in the surface of an arbitrary-shaped cavity subjected to a steady temperature field. Actually, not only is a general solution of this problem represented by Hankle function obtained for an arbitrary-shaped cavity, but also a process to calculate the coefficient of the dynamic thermal stress distribution in the surface of an arbitrary-shaped cavity is derived. For illustration, some numerical results of a circular cavity, an elliptic cavity, a lining horseshoe cavity and a square cavity are given.