A new, fast inversion approach for time-lapse seismic data is developed where the uncertainty of the inversion results is an integral part of the solution. The inversion method estimates changes in the elastic material properties of a reservoir because of production of hydrocarbons, including uncertainty bounds on these estimates. The changes in elastic properties then can be related to changes in hydrocarbon saturation and reservoir pressure by using rock-physics relations. The inversion operates directly on the difference between a repeat survey and a baseline survey. This is advantageous with respect to the uncertainty calculation, because an estimate of the seismic uncertainty can be obtained directly from the difference data in zones not affected by production. The method is formulated in a Bayesian setting, and the solution is represented by explicit expressions for the posterior expectation and the covariance of the elastic parameter changes. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Results of the applied approach to a real data set from the Norne field are consistent with the expected effects of water flushing because of water injection.