The effects of curvature radius(pipe diameter) and laser beam diameter on the initial instantaneous absorptivity of laser cutting for 304 stainless steel pipe and plate were investigated theoretically. The theoretical analysis showed that the pipe diameter D and the laser beam diameter d had important effect on the initial instantaneous absorptivity of laser cutting as the ratio of d to D is bigger than 0 866, and the initial instantaneous absorptivity of laser cutting increases with the pipe diameter (curvature radius) decreases or the laser beam diameter increases.