A general expression is derived for the effective attenuation of circular electric (TE01) waves owing to mode conversions in a section of wave guide whose shape deviates slightly in any specified manner from a perfect circular cylinder. Numerical predictions are in good agreement with experiment for the special case of transmission through an elliptically deformed section of pipe. The effect of random distortions in a long wave guide line is analyzed in terms of the mean‐square values of the Fourier coefficients describing the distortions; and from the general formulas it appears that the mode conversion losses depend in large measure upon the statistical distribution of the various types of distortion. Under certain rather arbitrary simplifying assumptions about this distribution, it is calculated that mode conversions in a 4.732‐inch copper pipe whose radius deviates by 1 mil r.m.s. from that of an average cylinder will increase the attenuation of theTE01mode at 3.2 cm by an amount equal to 8 percent of the theoretical copper losses. The dependence on frequency of mode conversion losses in such a guide is discussed.