Following the IPCC's report (2005), which recommended the development and the use of carbon capture and sequestration (CCS) technologies in order to achieve the environmental goals, defined by the Kyoto Protocol, the issue addressed in this paper concerns the optimal strategy regarding the long-term use of CCS technologies. The aim of this paper is to study the optimal carbon capture and sequestration policy. The CCS technologies has motivated a number of empirical studies, via complex integrated assessment models. This literature always considers that the existing technology allows sequestrating a fraction of the carbon emissions and concludes that the early introduction of sequestration can lead to a substantial decrease in the cost of environmental externality. But, the level of complexity of such operational models, aimed at defining some specific climate policies. We develop a very simple growth model so as to obtain analytical and tractable results and therefore exhibit the main driving forces that should determine the optimal CSS policy. We show within on the cost of extractions, CSS may be a long-term solution for the carbon emissions problem. Besides, it is also shown that the social planner will optimally choose to decrease the rate of capture and sequestration. Besides, we also introduce the decentralization of this simple economy, by considering the individual program of the fossil resource-holder and the one of the representative consumer. This helps us to compute analytically the optimal environmental policy, that is the also the optimal fossil fuel price profile.