The mechanical integrity of caprocks overlying injection formations is one of the key factors for safe storage of carbon dioxide in geological formations. Undrained effects caused by CO2 injection on strength and elastic parameters should be properly considered in the operational design to avoid fracture creation, fault reactivation and unwanted surface uplift. This study presents results from eleven undrained triaxial compression tests and one oedometer test on the Draupne shale, which is the main caprock of the Smeaheia site in the North Sea, to extract parameters relevant for seal integrity. Tests have been performed on samples oriented perpendicular to and parallel with the horizontal layering of the rock to study the effects of sample orientation relative to the loading direction. Results from undrained triaxial tests showed only minor effects of sample orientation on friction and cohesion. However, when loading during undrained shearing was parallel with layering (horizontal samples), measured Young’s modulus was roughly 1.4 times higher than for the vertical samples. Undrained shearing of vertical samples generated 30–50% more excess pore pressure than for horizontal samples with similar consolidation stress owing to more volume compaction of vertical samples. With apparent pre-consolidation stress determined from a high-stress oedometer test, the normalized undrained shear strength was found to correlate well with the overconsolidation ratio following the SHANSEP (Stress History and Normalized Soil Engineering Properties) procedure.