Observation spillover resulting from sensing signals often introduces structural instability of undamped structural systems. One method to prevent the spillover problem is to use spatially distributed modal sensors in which the effects of residual modes are filtered out. In this study, a modal filtering theory for a generic shell continuum, based on modal orthogonal functions, is derived. The sensor signals are contributed from membrane strains and bending strains of the piezoelectric distributed sensor on the shell continua. This theory is applied to a design of cosine shaped convolving sensors for a circular ring structure. Performance of the distributed convolving sensors is studied. Bending and membrane (circumferential) sensitivities of the convolving ring sensors are defined.