In this paper, the fundamentals of the SIF (Smooth Integral Formulation) were summarised. A numerical application of the SIF was proposed for an acoustical domain characterized by random boundaries, in order to illustrate the effectiveness of this approach on a wide frequency range. It was shown that in the low frequencies the SIF is able to precisely describe the successive modes and when the frequency increases the SIF prediction is able to give the trend of the strongly oscillating deterministic response. The SIF is then applied to the high-frequency domain. In this domain the number of unknowns can be reduced, because it is not necessary to calculate the first order moments, which may be fixed to zero. This enables to decrease the number of unknowns. The high-frequency SIF response is smooth and effectively gives the correct trend of the response in the high-frequency field, but peaks due to the low-frequency behaviour are removed from the response. Then, the original SIF was coupled with FEM for mid-frequency applications. For this purpose, it was assumed that: the mid-frequency range is the domain within which a structure is constituted of two parts, one with a low-frequency behaviour, the second with a high-frequency behaviour; the properties of a structure are intrinsically uncertain. This global uncertainty plays no role in the low-frequency field, on the other hand it has a large effect on the high-frequency responses. It was finally shown, that the mid-frequency field could be efficiently analysed by coupling the SIF with a FE approach. The entire formulation was derived for a structure made of two subsystems. This novel formulation was applied to a simple mid-frequency structure, a 2D acoustical domain coupled with a beam. The results show the effectiveness of the hybrid formulation: the deterministic peaks in the frequency response are perfectly described while the HF response is smoothened. This proves that the SIF formulation is a consistent formulation for vibro-acoustic analysis of uncertain structures, and its formulation can be coupled efficiently with a deterministic formulation for mid-frequency investigations obtaining an hybrid method.