Active sound control (ASC) based on surface potentials is one of two methods of noise control using potential-based method. The method does not require detailed knowledge of the noise source parameters, boundary conditions, characteristics of the acoustic medium or the transmission path. It allows significant volumetric noise cancellation inside the shielded region using only the knowledge of the total acoustic field which includes the wanted sound at the boundary of the shielded region(s) to obtain additional secondary sound sources known as controls which are distributed at the boundary of the shielded region. It allows the presence of a wanted sound inside the shielded region, which it preserves while canceling the noise. In contrast, other methods require various detailed knowledge. In many cases, they do not allow the wanted sound to be generated inside the protected region. The aim of this thesis is to implement numerically the ASC method in 3D bounded regions and confirm its theoretical predictions. The theoretical framework for the method has already been established in previous related literature. Experimental work in this area is mostly limited to laboratory experiments in one dimensional settings.The algorithm was tested in 3D numerical test cases in the frequency domain involving single and composite regions. The Helmholtz equation was used to model the wave propagation. In both single and composite regions, volumetric noise cancellation of over 20 dB was achieved at most areas of the shielded regions. Outside the shielded region, the field remained practically unchanged during noise cancellation. On the other hand, in test cases involving wanted sound, the noise inside the shielded region was canceled while the wanted sound was preserved. However, outside the shielded region, the field was amplified. Moreover in composite regions, the selective cancellation/propagation of the wanted sound was demonstrated successfully in regions having two and three sub-regions by allowing the wanted sound to propagate to one region but not to the other. To enforce selective propagation of the wanted sound, additional steps are required to obtain the separate field of the wanted sound in addition to the total field. A study on the effect of the number of controls on noise cancellation showed that in both single and composite regions, as the number of controls fell there was a corresponding decrease in the level of noise cancellation. A doubling of the number of controls yields about ~3 dB of noise cancellation, and vice versa. The independence of the operation of the algorithm on characteristics or number of noise sources, shape, size or position of shielded region is also demonstrated via further test cases. In all test cases considered, the results confirmed the theoretical predictions. However, at resonance modes the method did not provide noise cancellation, though at near-resonance modes a lower level of noise cancellation was obtained.Although this work considered only monochromatic waves, the method is applicable to broadband noise. In real-time application of the method, the assumption in the thesis that only the field of the noise source(s) is known does not hold and therefore its implementation is more complicated.