Based on the perturbation theory, two interval analysis methods named first-order interval parameter perturbation method (FIPPM) and high-order interval parameter perturbation method (HIPPM) were proposed for the coupled structural-acoustic system prediction with interval uncertainties in both system parameters and external loads. The structural-acoustic discrete equilibrium equation was established based on the finite element method. Interval variables are used to quantitatively describe the uncertain parameters with limited information. According to the first-order Taylor series and first-order perturbation theory, the response interval could be quickly evaluated by FIPPM. On the contrary, HIPPM introduced modified Taylor series to approximate the non-linear interval matrix and vector. Higher order terms of the Neumann expansion were retained to calculate the interval matrix inverse. By comparing the results with traditional Monte Carlo simulation, a 3D cuboid model was given to demonstrate the feasibility and effectiveness of the proposed methods to predict the sound pressure ranges of the coupled structural-acoustic systems.