This paper analytically demonstrates the use of multiple piezoelectric actuators bonded to the surface and point force actuators applied directly to a plate to reduce sound transmission through the plate. A harmonic plane wave incident on a simply supported, thin rectangular plate mounted in an infinite baffle was considered as the primary source. Both multiple piezoelectric and point force actuators are separately used as secondary (control) sources to attenuate the sound transmission through the plate. An optimal process was applied to obtain the input voltages of the piezoelectric actuators and the magnitude of the point forces, so that the radiated acoustic power can be minimized. Results show that a reduction of sound transmission through the plate is successfully; achieved, if the proper size, number, and position of the piezoelectric or point force actuators are selected. Additionally, a comparison showed that point force actuators provide more effective control of the sound transmission than piezoelectric actuators; however, piezoelectric patches have more practical implementation than point force shakers, because of their low cost and light weight.