The stress field around the tip of the blunt crack in rock-type materials under compressive loading is analyzed, and the relation of the stress field is set up. Compared to the stress field of the ideal mathematic crack, the effect on the distribution of the stress field by the thickness or the curvature radius of the blunt crack is considered. Based on the stress field, the two-parameter fracture criterion for the blunt cracks under compressive loading is set up. The two parameters in the criterion are related to the material property, and can be determined by the experiments or theoretical analysis. By the fracture model in the paper, the fracture analysis of the blunt crack under compression are carried out, and the theoretical results are in concordance with the experimental results, which shows the fracture criteria in the paper is available to the fracture analysis of the blunt crack.