Water-rock interaction has always been a hot topic of research. Water-rock interaction deteriorates rock properties and affects the strength of rock. In this paper, the strength and deformation of argillaceous dolomite undergone different dry-wet cycles are investigated through uniaxial and triaxial compression tests. Moreover, the damage statistic constitutive model of rock under dry-wet cycles is derived based on the continuous damage mechanics and statistical theory. Results reveal that: the peak strength of argillaceous dolomite declines with the proceeding of cyclic drying and wetting. In uniaxial compressive test, the total deterioration degree of argillaceous dolomite increases in general with the increase of dry-wet cycles, while the staged deterioration degree and average deterioration degree gradually reduces and tends to be stable. In triaxial compressive test, the total deterioration degree of argillaceous dolomite decreases before increasing with the climbing of confining pressure. Larger number of cycle has a greater effect on the deformation of rock than higher confining pressure does. The elastic modulus of argillaceous dolomite also declines basically with the proceeding of cyclic drying and wetting. Comparison between theoretical curves and experimental curves demonstrates that the constitutive model well reflects the triaxial stress-strain relationship of rock, hence is rational.