Fracture arrest in layered rock sequences is important in many geodynamic processes, such as dyke-fed volcanic eruptions, earthquake ruptures, landslides, and the evolution of plate boundaries. Yet it remains poorly understood. For example, we do not fully understand the conditions for dyke arrest (preventing potential eruptions) or hydraulic-fracture arrest in gas shales (preventing potential aquifer pollution). Here we present new numerical results on the conditions for arrest of fluid-driven (mode-I) vertical fractures in layered rock sequences when the tips of the fractures approach the interface between two layers of contrasting mechanical properties. In particular, we explore the stress-field effects of variations in layer stiffness, proximity of fracture tip to layer interface, and layer thickness. When the layer hosting the fracture tip is stiffer, fracture arrest normally occurs at the interface with the more compliant layer. By contrast, when the layer above the interface is stiffer, fracture arrest may occur within the host layer well below the interface. These conclusions are supported by field observations of arrested fluid-driven joints and dykes and, therefore, provide a better understanding of the mechanical conditions for dyke-fed eruptions.