Rectangular expansion chamber silencers are extensively used in the heating, ventilating and air conditioning (HVAC) ducts. The inlet and outlet openings excite higher-order modes inside the rectangular expansion chamber. An analytical formulation is proposed here to consider higher order modes as well as the flexibility of walls. The rectangular expansion chamber is modelled as a piston-driven rectangular cavity where the inlet and outlet ports are modelled as uniform velocity pistons. If the size of the piston is small compared to the wavelength, then the plane wave excitation is a valid assumption. A transfer matrix formulation has been developed for the yielding-wall rectangular chambers by considering the structural-acoustic coupling. It is presumed that the coupled response can be described in terms of finite modal sets of the uncoupled acoustic subsystem and the structural subsystem. Flexible walls of the rectangular expansion chamber are modelled as an equivalent unfolded plate to calculate the natural frequencies and mode shapes of the uncoupled structural subsystem. The velocity potential inside the chamber is expressed as superposition of the velocity potentials of two different configurations. The first configuration is a piston source at the inlet port and a rigid termination at the outlet, and the second one is a piston at the outlet with a rigid termination at the inlet. Pressure inside the chamber is derived from the velocity potentials using the linear momentum equation. The transfer matrix is derived from the average pressure values, and thence the transmission loss is calculated. This method is validated by means of the FEM results. It may be combined readily with the transfer matrices of the other constituent elements upstream and downstream in order to compute the overall transmission loss or insertion loss of the entire system.