This paper presents the results of adding a CCS(Carbon Capture and Storage) plant including an underground CO2 storage to a well described and well documented vision of converting the present Danish fossil based energy system into a future sustainable energy system made by the Danish Society of Engineers. The analyses point in the direction that in such context a CCS investment is not a suitable way to decrease CO2 emissions. Other alternatives are more cost effective and will fit better into the long-term implementation of sustainable energy systems. The reason is that CCS investments involve huge construction costs with the expectation of long lifetimes. Consequently, the CCS has to operate as part of large-scale power or CHP plants with high utilisation hours for the CCS investment to come even close to being feasible. However, seen in the light of transforming to sustainable energy systems, the number of utilisation hours of power and CHP plants will have to decrease substantially due to the energy efficiency measures in combination with the inclusion of renewable energy power inputs from wind and similar resources. Consequently, no power or CHP plants exist in future sustainable energy systems with sufficient utilisation hours to justify a CCS plant.