An accurate heat-transfer analysis of reactor fuel elements requires an accounting of the axial heat-conduction effects. The exact treatment requires the solution of a boundary-value problem involving partial differential equations. In this paper, an approximate method is developed for determining the axial and transverse heat-flux distributions in reactor-fuel elements. The method is analogous to the Karman-Pohlhausen method of boundary-layer theory. When the results of the approximate method are compared with those of known exact solutions, the agreement is found to be excellent. Two examples are given in which the approximate method gives values that agree with the exact solutions to within about 2%.