Time-lapse seismic data acquisition and processing is a mature technology to monitor changes of rock properties due to hydrocarbon production. The same efficiency is expected from this technology to monitor carbon dioxide (CO2) injected in underground reservoirs. Since 1996, Statoil has injected more than 11 million tons of CO2 in a saline aquifer of the Sleipner field (Norwegian North Sea). This Carbon Capture and Storage (CSS) industrial pilot is now considered as an international reference site. To insure an accurate monitoring, seismic surveys are carried out every two years or so, thus providing the research community with an exceptional series of 3D seismic datasets. In order to further characterize the CO2 injection into the Sleipner saline aquifer, we present here the results of a joint stratigraphic inversion of time-lapse seismic data. This approach has been applied to the 1994 and 2006 vintages to obtain detailed estimates of the elastic parameters within the aquifer. After a presentation of the joint pre-stack stratigraphic inversion methodology, we focus on the quantitative analysis of the inverted elastic parameters to demonstrate the efficiency of the joint inversion with respect to independent inversions of the successive datasets.