Uncertainties in the location, geometry and flow properties of faults can have a significant impact on the reservoir volumes, well planning, and production predictions. However, the reservoir geometry is usually fixed to a single interpretation in history-matching workflows due to the complexity of automatic updating of the structural framework and the related simulation grid.In this paper, we propose a method to handle fault geometric uncertainties in the reservoir model and present an assisted history-matching workflow for updating the structural model with the Ensemble Kalman Filter (EnKF).An ensemble of reservoir models, expressing explicitly the uncertainty in the throw and position of faults, is created. To avoid rebuilding the grid at each update step, we propose an elastic grid approach, where the geometry of a base-case reservoir grid is deformed to reflect the alternative structural realizations. The fault throw and fault position are considered as parameters for assisted history matching and are updated by sequential assimilation of production data using the EnKF.The method is applied to synthetic examples and promising results are obtained. The result is an ensemble of history-matched structural models with reduced and quantified uncertainty in the fault position and throw. The elastic grid approach and the sequential processing of measurements in the EnKF provide a setting for fast and continuous model updating.