An analytic solution for transverse electric mode scattering from a parallel-plate waveguide with periodic grooves is obtained. The Fourier transform is used to express the scattered field in the spectral domain as superposition of the parallel-plate waveguide modes. The simultaneous equations are solved to represent the transmitted field in series form which is very efficient for numerical computation. When we use the residue calculus, the reflection and transmission coefficients are obtained, and their bandstop filter characteristics are studied in terms of frequency and groove sizes. ¿ American Geophysical Union 1994