Three-dimensional acoustic finite elements have been applied to calculate the ‘knock-induced’ cavity resonances for combustion chambers and the cavity ‘booming’ frequencies for passenger compartments. The NASTRAN finite element program is employed to solve the acoustic free-vibration problems, and resonant frequencies obtained from these numerical predictions have been compared with experimental results. In addition, the resonant mode shapes are shown and illustrate the acoustic pressure distributions and nodal surfaces for particular resonant frequencies.Besides a prismatic passenger compartment with ‘bench-seat’ model, this paper also presents results for a general ‘bucket-seat’ model with irregular cross-sectional seat contours. Moreover, a rather complicated cavity model such as a combustion chamber is included to illustrate the capabilities of the finite element analysis. The results illustrated in this paper are of interest in combustion chamber thermodynamic property studies, knock-sensor designs, and vehicle interior noise studies.