The radiant efflux from a cylindrical cavity having nonisothermal bounding surfaces is determined by solving a problem of combined radiation and conduction. The cavity may be visualized as a circular hole machined into the exposed face of a solid, with the solid being heated uniformly from behind. A two-dimensional temperature distribution is set up in the solid owing to radiative heat losses from the cavity and from the exposed face of the solid. A solution method is employed whereby the radiation and conduction problems are dealt with successively. Results are obtained, for parametric values of the cavity emittance and depth-radius ratio and of a group which fixes the axial temperature variation. The results indicate that the radiant efflux from the cavity increases with increasing values of the aforementioned parameters. The effect of the presence of the cavity is confined to a region of the solid whose depth, and radius are, respectively, twice and four times the depth and radius of the cavity.