Studies of oil reservoirs show that unconformities may occur between the reservoir and the caprock. At the boundary where the unconformity occurs, there may be a layer of higher permeability compared to the caprock. Such traps may occur at CO2 storage sites and, therefore, their effect should be investigated. In this work, we simulate CO2 storage beneath angular unconformities, where sandstone layers have been tilted and eroded prior to the deposition of a caprock. After preliminary studies into the effect of gridding such traps, we describe simulations of a range of 2D and 3D models. The results reveal that migration of CO2 is influenced by the lithology beneath the unconformity, which could have been modified by weathering or diagenesis. This can have both positive and negative effects on the CO2 storage capacity and security. It shows that an unconformity model that has a layer of high permeability at the interface between the aquifer and the caprock, as a result of weathering or diagenesis, can contribute to pressure diffusion across the reservoir. This could improve CO2 sequestration by providing pathways for CO2 migration to access other parts of the storage complex. However, this could also have a negative effect on the security of CO2 storage by providing pathways for CO2 to migrate out of the storage formation and so increase the risk of CO2 leakage.