We investigate how existing veins interact with extension fractures in rocks using 3-D Discrete Element Method models with a geometry inspired by tension tests with notched samples. In a sensitivity study, we varied (a) the angle between the vein and the bulk extension direction and (b) the strength ratio between host rock and vein material. Results show a range of vein-fracture interactions, which fall into different, robust, “structural styles.” Veins, which are weaker than the host rock, tend to localize fracturing into the vein, even at high-misorientation angles. Veins, which are stronger than the host rock, cause deflection of the fracture tip along the vein-host rock interface. Fractures are arrested at the interface from weak to stronger material. When propagating from a stronger to a weaker material, macroscopic bifurcation of the fracture is common. Complex interactions are favored by a low angle between the vein and the fracture and by high-strength contrast. The structural styles in the models show good agreement with microstructures and mesostructures of crack-seal veins found in natural systems. We propose that these structural styles form the basis for criteria to recognize strength contrasts and stress of crack-seal systems in nature.