For radial steady‐state heat flow through hollow circular cylinders, the usual application of thermoelastic theory indicates that the heat flow per unit length to cause fracture (Wmax) is simply the product of two factors:M, characterizing the material, andS, the shape. Studies sponsored by the Atomic Energy Commission are in progress at Battelle Memorial Institute to evaluate the practical worth of this relationship. In this paper, attention is given to its validity for cylinders with both circular and noncircular cross sections and to measuring the effect of dimensions onSfor circular cylinders. Thermal fracture experiments on circular cylinders of two ceramics indicated the manner in whichSvaries with the ratios of dimensions which define the shape. Changing all dimensions by factors up to 1.6, with these ratios constant, had no noticeable effect onS.Using theorems derived by Biot, it is shown that the product relationship is expected to hold for a considerably wider variety of shapes than the simple circular tube. Experimental results from tubes having cross sections with a circular inner boundary and a circular or square outer boundary support the product relation. Information was obtained on the shape factor for these cross sections and for similar tubes with a triangular outer boundar