A fibrous rare earth selective emitter is approximated as an infinitely long, cylinder. The spectral emittance, e(sub x), is obtained L- by solving the radiative transfer equations with appropriate boundary conditions and uniform temperature. For optical depth, K(sub R), where alpha(sub lambda), is the extinction coefficient and R is the cylinder radius, greater than 1 the spectral emittance depths, K(sub R) alpha(sub lambda)R, is nearly at its maximum value. There is an optimum cylinder radius, R(sub opt) for maximum emitter efficiency, n(sub E). Values for R(sub opt) are strongly dependent on the number of emission bands of the material. The optimum radius decreases slowly with increasing emitter temperature, while the maximum efficiency and useful radiated power increase rapidly with increasing, temperature.