Natural fractures are abundant and important components in many carbonate sedimentary rocks globally. In hydrocarbon and groundwater reservoirs of carbonate rocks they can form connected networks and thereby influence the permeability and f luid flow significantly. Outcrop studies of fractured carbonate rocks can provide an essential understanding of 3-dimensional fracture networks, thereby aiding in understanding fracture patterns and connectivity in subsurface carbonate reservoirs. The Arnager Limestone Formation is a naturally fractured silica-rich chalk of Coniacian age exposed in a coastal cliff on the island of Bornholm in the Baltic Sea (Denmark). This study examines the natural fractures in the Arnager Limestone Formation from a structural and geomechanical perspective. The Arnager Limestone Formation forms one, 12–20 m thick, main rock mechanical unit; bedding planes acts as weak interfaces and divides it into near-identical, cm- to dm-thick rock mechanical subuits. Flat-lying (horizontal) or low-angle dipping bedding-parallel fractures are intersected by two near-vertical or steeply dipping fracture systems, a major N–S-trending system and a less prominent W–E-trending fracture system. Rock mechanical analysis of the tensile strength and elastic moduli provides the foundation for discussing maximum burial depth of the Arnager Limestone Formation. The tensile strength gives information on the bedding-parallel fractures, which can have formed due to stress relief during uplift and erosion, possible accentuated by glacial processes. The near-vertical fracture sets are interpreted to have formed in response to tectonic movements.