The paper deals with the optimal design of circular arches against creep buckling in Rabotnoov-Shesterikov sense. Fundamental buckling modes corresponding to two lowest critical loads both for out-of-plane and in-plane buckling of the arch are studied. Both depth and width of a rectangular cross-section are treated as independent control functions. The design variables are determined so as to minimize the total volume of an arch under given external load (radial pressure) and the critical time. The effect of the behavior of loading in the course of buckling on optimal shapes is analyzed. The problem is solved by the use of Pontriagin’s maximum principle.