Active noise cloaking of rigid and elastic 2D cylindrical shells in an infinite acoustic medium is presented. The control approach utilises control sources or forces and discrete error sensors at which the desired field is specified. The optimal complex control source amplitudes are determined from minimisation of a quadratic cost function and a priori knowledge of the incident sound field. For the case of the rigid cylinder, the scattered field due to an incident plane wave is actively attenuated using monopole sources and error sensors arranged circumferentially around the scatterer. For the case of the elastic cylindrical shell, the scattered and radiated fields are actively attenuated at the shell circumferential modes using either monopole control sources in the exterior fluid or point control forces applied directly to excite the shell. Active cloaking using control forces to modify the structural response, herein termed active structural acoustic cloaking, is found to result in simultaneous cloaking of both the interior and exterior fields, attributed to direct coupling between the vibrating shell and the interior and exterior fluids. An approach to identify the number of control sources/forces and error sensors for active cloaking within a predefined error is also described.