As a good supplement of conventional acoustic radiation modes (a-modes), a set of so-called “structure-dependent radiation modes” (s-modes) is introduced to describe the sound power radiation from a vibrating structure. Differing from a-modes, s-modes are determined by not only the acoustic resistance matrix of the structure but also the frequency-independent normal modes of the structure. Such a new definition has the following main advantages over the conventional one: (1) it can reflect directly the influences of dynamic properties (e.g., boundary conditions) of the structures on its sound power radiation; (2) the number of s-modes generated is generally less than that of a-modes since the former depends on the number of structural modes involved in the vibration while the latter depends on the number of segmented elemental radiators of the structure, and consequently, the demand for large data storage can be greatly alleviated, especially for large structures and/or higher frequency vibrations; (3) the set of s-modes possesses a better convergence than that of a-modes because the higher ordered s-modes can decay more rapidly than the same ordered a-modes. Two baffled, finite, models, i.e., a simple beam and a thin plate, are employed to investigate numerically the acoustic properties of s-modes, and then compared with those of a-modes. It has been shown that the two sets of radiation modes share a very similar frequency-dependent behavior in that the radiation efficiency falls off very rapidly with increasing mode order at low frequency range (typically with kl<1). Meanwhile, the number of s-modes required to describe the total sound power radiation is found to be the same as that of a-modes. Consequently, an appropriate truncation of a-modes can be achieved by using the number of vibrational modes involved. Nevertheless, the odd-ordered (even-ordered) s-modes are found only associated with the odd-numbered (even-ordered) structural modes. In case of only few of the s-modes dominating, each s-mode tends to be largely affected either by the same ordered structural mode for a non-resonant frequency or by the resonant mode for a resonant frequency. As a result, the coupling relations between the dominating radiation modes and the associated structural modes can be revealed explicitly. In general, s-modes are recommended to be used to describe the sound power radiation from a vibrating structure whose geometry sizes are much larger than the acoustic wavelength, should its structural modes and the associated modal amplitudes have been somehow obtained.