It is well known that flexural vibration on a flat plate stiffened by periodically placed line supports shows stop/passband behavior in frequency, associated with Bloch waves. For a one-dimensional situation, with plate vibration incident normally on the ribs, a simple model in which the ribs exert forces normal to the plate by virtue of their mass often suffices to explain stop bands that occur when the rib spacing d accommodates an integer number of the half-wavelengths of plate vibration. This paper presents results for cases where the ribs present normal forces as well as moments to the plate. Particular attention is paid to the case where the rotary impedance offered by the rib is limited by the rib’s own flexibility in bending. At special antiresonance frequencies associated with the rib’s own bending motion, the rib rotary impedance is seen to rise sharply and to give rise to stop bands additional to those generated by the rib normal forces.