The concept of a weak sound radiating cell is proposed to reduce the low frequency radiated noise from structures. The cell consists of two coupled surfaces such that, when placed on a vibrating structure, the responses of the two surfaces are nearly out-of-phase and of equal strength over a wide frequency range. This structure response leads the cell to behave as an acoustic dipole and thus as a poor sound radiating source. The control of low frequency structurally radiated noise is then achieved by covering the structure with an array of these weak radiating cells, i.e. surface treatment. Thus, the surface treatment essentially transforms the response of the structure to that of a distributed array of dipoles yielding a low sound radiating structure. Theoretical models are developed to predict the performance of the cell. Experimental verification is performed for a single cell applied to a piston-like structure to demonstrate the concept on a simple radiating structure. The results demonstrated an overall sound power level reduction of 5.2 dB between 400-1600 Hz with maximum reductions over 30 dB at discrete frequencies. Finally, an array of weak radiating cells is experimentally applied to a more complex structure, a rectangular plate. The results of the plate experiments reveal an overall sound power level reduction of 10.2 dB between 100-1600 Hz with maximum reductions of 25 dB at discrete frequencies. These results demonstrate the potential of the weak radiating cell concept to reduce low frequency structurally radiated noise.