This article offers some economic insights for the debate on the reversible geological disposal of radioactive waste. Irreversibility due to large sunk costs, an important degree of fiexibility and several sources of uncertainty are taken into account in the decision process relative to the radioactive waste disposal. We draw up a stochastic model in a continuous time framework to study the decision problem of a reversible repository project for the radioactive waste, with multiple disposal stages. We consider that the value of reversibility, related to the radioactive waste packages, is jointly affected by economic and technological uncertainty. These uncertainties are modeled, first, by a 2-Dimensional Geometric Brownian Motion, and, second, by a Geometric Brownian Motion with a Poisson jump process. A numerical analysis and a sensitivity study of various parameters are also proposed.