Upstream interactions between two premixed flames of butane and air are investigated numerically by solving the problem of two unsteady one-dimensional flames propagating toward each other. Premixed flames of three types at varied ratios of fuel to oxidizer, i.e., lean, stoichiometric and rich premixed flames, are adopted to evaluate the influence of Lewis number during the process of upstream interaction. The results reveal that the nature of upstream interactions is dominated by the Lewis number of deficient reactant (effective Lewis number) in a combustible gas. The burning rate for Le > 1 (fuel-lean) is accelerated during upstream interaction, whereas the burning rate is decelerated for Le < 1 (fuel-rich). For interacting butane/air premixed flames at a stoichiometric ratio, the burning rate is slightly accelerated. These accelerative and decelerative phenomena of burning rates are interpreted appropriately from the aspect of total effective enthalpy (thermal energy plus effective chemical energy).