Total acoustic power radiation from one side of a rectangular flat plate, vibrating in one of its natural modes under mixed boundary conditions, has been investigated here. The conditions at the edges of the plate that have been investigated here include – (i) two opposite ends fixed and other two free, (ii) one end fixed and other three free. Radiation efficiency of a rectangular flat plate, with two opposite ends fixed and other two free, has also been found to check the soundness of the method employed by comparing the radiation efficiency with the results available in literature. Numerical results on acoustic power radiation by the plate with different set of values of thickness ratio, aspect ratio and mode orders have been obtained. The characteristics beam functions developed by Warburton [1] have been used to define the deformation mode of the vibrating plates. When a plate with two opposite ends fixed and two free vibrates in one of its natural mode, acoustic power radiation increases in regular fashion with increasing mode order. But at the higher mode orders, it fluctuates maintaining nearly the same average magnitude and the waviness is gradually reduced as the mode order increases. In the case of a plate with one end fixed and other three free, power radiation is more than that of a plate with two opposite ends fixed and other two free. But the variation of power radiation with the change of mode order, thickness ratio, and aspect ratio is similar.