Loudspeaker cabinet design has historically been constrained by conventional manufacturing methods, which favour rectangular panel construction due to its simplicity and repeatability. Large Format Additive Manufacturing (LFAM) removes this constraint by enabling complex curvatures and geometries at manageable production costs. This introduces new possibilities for geometry-driven acoustic performance improvement, but also new challenges. In particular, the anisotropic material properties of 3D-printed polymers and a general lack of research on vibroacoustic behaviour in this context. This thesis develops a computational framework for simulating and optimising the vibroacoustic performance of sealed, low-frequency loudspeaker cabinets. The core problem is the coupled interaction between structural vibrations of the cabinet panels and the acoustic field they radiate, which is a multiphysics problem that requires numerical methods to solve. A hybrid FEM/BEM simulation model is implemented in COMSOL Multiphysics, combining finite element structural analysis with boundary element acoustic radiation modelling. The framework is validated against anechoic measurements of a physical prototype provided by partner Addit Audio. The validated simulation model is integrated into a gradient-based shape optimisation framework. Cabinet panel geometries are parameterised and iteratively deformed to suppress panel resonances and improve sound dispersion, using adjoint sensitivity analysis to efficiently compute gradients. Manufacturability constraints imposed by the LFAM process are incorporated throughout. The optimisation is applied to a rectangular reference cabinet, and the results are analysed in terms of physical mechanism, robustness, and transferability. The findings are broadly applicable to the vibroacoustic optimisation of thin-walled structures beyond the loudspeaker domain, wherever panel resonances and radiated sound are of concern.