TX 75083-3836, U.S.A. fax 01-972-952-9435. AbstractBuilding reservoir geological models that are consistent with all available information is necessary to reduce uncertainties in production forecasts. The stochastic/geostatistical approach is the only feasible way of integrating all kinds of data ranging from the geological knowledge to the production history. A stochastic model is chosen that accounts for geological knowledge, and geostatistical simulation provides realizations of the stochastic model. These realizations can be conditioned to static data at well locations to reduce the model uncertainty in the area where data are available.All along the different stages of a field life more and more dynamic data are available. This paper addresses the issue of generating model realizations that account for available dynamic data to further reduce uncertainty in the underlying geological model. A general tool has been developed to build geostatistical realizations that match both the available geological and dynamic data. The core of this tool is the Gradual Deformation Method that allows consistent modification of a realization in a continuous way. This method can be combined with a nonlinear optimization method for constraining realizations of a stochastic model to dynamic data. This approach is operational for Gaussian or non-Gaussian pixel based models. Model realizations can be deformed globally or locally while preserving the geostatistical characteristics. Several examples are provided to illustrate different features of the gradual deformation approach.