An indirect boundary element method using the concept of layer potentials and Kirchhoff-Helmholtz integral equation is formulated to analyze the couplin g between connected cavities. The indirect boundary element method is suitable in solving the internal and external acoustic radiation and scattering problem simultaneously and is based on the Huygen's principle in the physical sense. A computer program is made for formulated and discretized indirect BEM and its accuracy and applicability are tested for several examples including regular and irregular shapes. In order to analyze the acoustic coupling between two connected cavities, the junction constraint technique using Lagrange multipliers is studied. As an example, the acoustic coupling between passenger and luggage compartments through the loudspeaker hole is investigated. It is observed that some resonant frequencies are changed due to coupling. The shift in the first resonance frequency can occur when the rigid partition between two cavities is happen to be located at the pressure node of the combined cavity system without partition. Predicted acoustic transfer functions are compared with experimental ones and they agree reasonably well. In order to investigate the physical nature of this problem more clearly, the effects of a rigid partition within the rectangular cavity are studied varying the height, inclination angle, location, aperture size. The shift of resonant frequency is mainly affected by the location of the partition in the major axial direction of the whole chamber. If the partition is located at the pressure node of a mode, i.e. the region of maximum particle velocity, the resonant frequency is changed drastically. On the other hand, if the partition is located at the pressure antinode of a mode, i.e. the region of zero particle velocity, the resonant frequency is not changed. The results of present study would be very helfpul in the noise control of vehicles and in designing the barriers in the interior spcae.