We have developed a 2D axi-symmetric numerical model for an inductively coupled plasma system in order to analyze gas mixing effect through a narrow gap shower head. For frictional flow, holes of 0.5 mm diameter and 2 mm length are approximately modeled in 2D. Gas velocity distribution 10 mm below the shower head showed 2 times difference between the center and the edge at 10 mTorr. At 10 mm above the wafer, it was increased to 6 times difference due to the pumping duct effect. The model with a 5 mm height buffer region of a shower head showed reasonable behavior of Ar discharge. The density of Ar metastable showed additional peak inside the buffer region around the edge holes.