A numerical study on the structure of the laminar premixed flames established on perforated plate burners is performed. Three dimensional numerical simulations are performed on different perforated plate geometries, under various operating conditions, using methane reaction mechanism consisting 36 species and 253 reactions. The comparison of numerical results of inline and staggered configurations of perforated plate burner models show that the flame interaction has significant role in the structure and stabilization of perforated burner flame. The flame structure, flame height and the standoff distances are studied for both inline and staggered configurations at fuel lean and rich conditions. The flame standoff distance and the flame height found to be higher for staggered configuration in comparison to the inline configuration. The flame structure is studied for different hole-to-hole distances. The numerical results show an increase in flame base curvature with an increase in hole-to-hole distance for both inline and staggered configurations. The flame thickness reduces with an increase in hole-to-hole distance for both inline and staggered cases. The effect of recirculation and flame base curvature causes the flame base to get stabilized at a higher distance in staggered configuration in comparison to the inline configuration.