In this study the methane/air combustion in an industrial non-premixed burner was modeled and simulated. The burner is wall-fired type to generate a flat or rectangular flame with a large surface area so that heat effectively radiate towards tubes in a pyrolysis furnace. Computational fluid dynamics was utilized along with mass and energy transfer equations. The effect of burner geometry on the flame shape was investigated through simulation using the model. The burner variation includes standard main fuel inlets and the main fuel inlets which are closer to the fired wall with various wing fuel inlet slopes. Simulation results show that the burner with 68° wing fuel inlet produces a flame widening from the wing fuel inlet, but being not uniform in the vertical direction. The burner with 60° wing fuel inlet generates a uniform temperature profile in the vertical direction, but the flame is not as wide as that produced by the burner with 68° wing fuel inlet.