The material used is a commercial magnesium based alloy AZ31(Mg-3Al-1Zn) sheet with a thickness of 0.8 mm. Friction tests at various temperatures(R.T. to $200^{circ}C$) and at various holding forces in the 4 type molds were carried out to investigate the coefficient of friction. A warm drawing process with a local heating and cooling technique was developed in the Mg alloy sheet forming to improve formability because it is very difficult for Mg alloy to deform at room temperature by the conventional method. So, the coefficient of friction at various mold surface treatment conditions in this study was needed to develop the Mg alloy sheet forming technology.