Liquid nitrogen (LN2) cryotherapy can lead to fracture propagation, and affect the macroscopic mechanical property of coal. To explore the influence of LN2 cryotherapy on coal mechanics, LN2 cryotherapy was applied for the anthracite and coking coal samples. Then, the stress-strain curves of non-cryogenic coal samples and LN2 cryogenic coal samples were acquired based on uniaxial compression test. Based on damage variable evolution rule, the strength statistical damage (SSD) constitutive model considering the whole process of stress-strain curve was established. The results showed that the elasticity modulus, compressive strength, brittleness index of LN2 cryogenic anthracite and coking coal were decreased compared with the non-cryogenic coal samples, respectively. Based on the test results the damage evolution rule was obtained and the constitutive model parameters were calculated. The rationality of SSD constitutive model was verified through comparison of SSD modeling results, Mazars modeling results, and test results. After LN2 cryotherapy, the coal samples changed from brittleness to ductility, which is mainly due to that the cohesive force decreased and friction force increased in loading process. In the SSD model, parameter m represents the brittle characteristics. The brittleness index decreased with the decreased of m value. This study provides a theoretical support for LN2 cryogenic technology.