Due to the influence of geological structure, undulating structural planes (such as torsional fold surface) often occur in rock mass engineering. Due to the complexity of shape, the research on fracture and damage constitutive law of rock mass with undulating joints is not conducted fully. Undulating joints with different dip angles were fabricated using 3D printing technology. Uniaxial compression test and digital image correlation (DIC) technology were used to study the mechanical and fracture characteristics of undulating joint specimens. And based on the principle of fracture mechanics, an idea using DIC displacement field to solve the stress intensity factor (SIF) at the joint tips and further to study the damage constitutive law is firstly proposed. The results show that: the upper limit of undulating joint damage to specimens is determined with 46.6% through the minimum strength analysis. The sensitivity of undulating joint specimen uniaxial strength to joint dip angle is greater than that of straight joint specimen. The initiation of fracture occurs near the peak stress. The fracture process can be divided into the initiation and synchronous penetration of microcracks on the fracture path. And the fracture mode shows a combination mode of multiple tension and shear fractures. The stress intensify factor (SIF) increases with loading in the pre-peak stage, and the cracks propagate in shear at the joint left and right tips in the post peak stage, because of KII＞KI under the same stress. The undulating joint damage to specimen with the dip angle is in a sinusoidal curve, and the relationships between the total damage coupled by joint and load with strain are all "S" curves.