The response of burner-stabilized flat flames to acoustic perturbations is studied numerically. So far, one-dimensional models have been used to study this system. However, in most practical surface burners, the scale of the perforations in the burner plate is of the order of the flame thickness. This is expected to disturb the one-dimensional behavior and the main effects are studied using a 2-D numerical model. The numerical setup involves the set of 2-D transport equations for low-Mach number reacting flows using a simple reaction mechanism. After a short review of the physical phenomena observed so far in one-dimensional flames, the effect of a finite width of the perforations in a perfectly cooled burner is investigated for steady and unsteady flames in a 2-D micro-slit configuration. The influence on the acoustic response is also studied and the results are compared with one-dimensional calculations using volume-averaged models for the heat and mass transfer in the perforated burner plate to incorporate the 2-D effects. This last study shows that effective one-dimensional models are not able to incorporate all 2-D effects due to the presence of the burner plate in the flow. The acoustic transfer matrix can be applied to the stability analysis of acoustic systems with a porous or perforated surface burner. The most interesting application is the acoustic behavior of central heating systems.