This article describes a numerical study of the interactions between two lean premixed flames subjected to external acoustic forcing. This provides insights into the flame-to-flame interactions that may occur during combustion instability in annular combustors. Experimental measurements for comparison are available from the target combustor developed at Cambridge University (Worth and Dawson, 2012). Large eddy simulation is applied using the open source computational fluid dynamics toolbox, OpenFOAM, with the combustion modeled using the partially stirred reactor model with a four-step chemical reaction mechanism for methane/air. Harmonic velocity oscillations are imposed at the inlet; the flame responses are studied based on heat release rate signals in different combustion regions. The effect of the flame separation distance (S-d) on both the flame dynamics and unsteady heat release responses is analyzed. The results show that the flame-to-flame interactions are nonlinear for the flame separations studied. The spatial variation of the unsteady heat release rate demonstrates that flame-wall interactions play an important role, becoming even more important than flame-to-flame interactions for closely spaced flames (S-d < 2.00D). These findings imply that for the flame separation distances studied, any flame model used in the low-order annular combustion instability prediction should account for both nonlinearity and flame-to-flame interactions.