Abstract-High power, high frequency microwave radiation can be transmitted with very low loss in oversized corrugated metallic waveguide. We derive a linearly polarized (LPmn) mode basis set for these waveguides for the special case of quarter wavelength depth corrugations. We also show the relationship between the LPmn modes and the conventional modes (HEmn, EHmn, TE0n, TM0n) of the corrugated guide. The loss in a gap or equivalent miter bend in the waveguide is calculated for single mode and multi-mode propagation on the line. In the latter case, it is shown that modes of the same symmetry interfere with one another, causing enhanced or reduced loss, depending on the relative phase of the modes. If two modes with azimuthal (m) indeces that differ by one propagate in the waveguide, the resultant centroid and the tilt angle of radiation at the guide end are shown to be related through a constant of the motion. These results should be useful in describing the propagation of high power, linearly polarized radiation in these overmoded, corrugated waveguides.