A three-dimensional linear acoustic analysis has been developed to study the combustion instabilities in systems with complex geometries and non-uniform distributions of mean flow properties. The formulation is based on a generalized wave equation derived from the conservation equations for two-phase mixtures. To account for the configuration and property variations, the chamber is discretized axially into a number of cells, within which the axial flow properties are assumed to be uniform. A combined modal-expansion and spatialaveraging technique is then applied to treat the unsteady motions in the transverse plane of each cell. Finally, the oscillatory flow properties are matched at the interface of each pair of adjacent cells. This procedure eventually leads to the determination of the stability characteristics of the system in terms of the oscillatory frequency and growth constant. The analysis has been carefully validated against several well-defined problems for which either analytical or numerical solutions are available. A parametric study is conducted to investigate the various mechanisms for driving combustion instabilities in laboratory combustor.