Measurements of the growth and size distribution of electron avalanches have been made in methane gas, over a pressure range from a few torr to 14 atm absolute, which show that field distortion due to a hole in the anode influences the growth of avalanches occurring at high gas pressures and at values of electrode separation ≤ 0.5 cm. The degree of influence depends on the size of the anode hole and on the value of E/p0.