The transient vibration and sound radiation (TVSR) of plate-like structures with general elastic boundary conditions was investigated using the time-domain finite element method (TDFEM) and time-domain boundary element method (TDBEM). In this model, the structure can have arbitrary elastic boundary conditions and hence the effects of the boundary conditions on the TVSR can be effectively studied. The predicted results agreed well with existing experimental data using two classical boundary conditions: simply supported at all edges and clamped-free-free-free. The TVSR of a single panel with a more general boundary condition in two connected chambers was also measured. The predicted results agreed well with these experimental results. The prediction method was subsequently applied to evaluate the effects of elastic boundary supports on the TVSR of a window caused by a sonic boom. Loudness, non-audible acoustic perception, and tactile vibration thresholds were analyzed for different boundary conditions (varying between clamped and simply supported). The possibility of improving the transient vibration and noise isolation performance by selecting an appropriate boundary condition was thereby demonstrated.