The development of a Linearized Euler Equation (LEE) model for analyzing high frequency longitudinal combustion instability is described. The model includes mean flow effects and is generalized for multiple domains as well as natural boundary conditions that deviate from acoustically perfect conditions. These effects are systematically evaluated. Calculated spatial mode shapes and resonant frequencies are compared to experimental measurements and good agreements are obtained. Demonstrative results using a prescribed unsteady heat release model are also analyzed. Observations made from analytical results include mean flow decreases resonant frequencies and shifts the antinode locations; effects of entropy wave and mean flow property changes are location-dependent; application of natural boundary conditions produces more resonant modes and shifts the nodal locations; and the primary effect of unsteady heat release is a change in the linear growth rate. The LEE model is shown to be a useful platform for developing appropriate combustion response functions.