Abstract: In order to study the theoretical relationship between the material removal rate and the laser cutting process parameters under the model of Fiber laser nitrogen melting cutting, a mathematical model which is based on dimensional analysis method is established, Then, a single-factor laser cutting experiment was carried out on SUS304 stainless steel with a thickness of 3 mm by a fiber laser cutting machine with a power of 3 000 W, and the variation law of cutting comprehensive parameters in the model was determined. According to the analysis of the experimental results and the model, it is shown that the effect of the removal coefficient on the molten slag height is mainly determined by the critical value of the focus position. When the focus position is greater than this critical value, they are positively correlated, otherwise they are negatively correlated; Whether the material can be penetrated depends on the comprehensive parameters of laser cutting. There are different critical values of laser comprehensive parameters at different focus position. For 3 mm stainless steel, the minimum critical value appears at the focus position of 1 mm, with the size of 42.76.