[Objective] Rock material typically exhibits nonlinear strength characteristics under complex loading conditions, and stress-drop can be observed during shear failure while retaining part of the residual strength. To investigate the mechanical properties of carbonaceous shale, conventional triaxial compression tests were conducted, and a new rock damage model was established based on continuum damage mechanics to describe the stress-strain curves. [Methods] The proposed model first utilized a nonlinear exponential strength criterion to describe the micro-elements of rocks, considering the material heterogeneity, and assuming the micro-element strength followed a Weibull distribution. The damage variable was derived from the accumulated failure proportion of micro-elements. Subsequently, the model employed a modified Lemaitre equivalent strain assumption to capture the stress-drop effect and residual strength, allowing for the entire stress-strain curve to be represented. Model parameters were determined using the extremum method. Finally, the model’s predictions were compared with conventional triaxial compression test results from different rock types to verify its validity. [Results] Results showed that the established rock damage model accurately described the entire stress-strain relationship of rock samples under various confining pressures. During the post-peak deformation stage, the shear strength of the rock samples dropped rapidly and eventually approached the residual strength due to the stress-drop effect, and the rock samples became fully damaged. The comparisons also suggested that the exponential strength criterion was generally suitable for various rocks; however, both the axial strain corresponding to peak strength and the residual strength varied approximately linearly with confining pressure. [Conclusion] The established exponential damage model of rock has good prospects for theoretical application.