Variation simulation is one important activity during early product development. It is used to simulate the statistical distribution of assemblies or sub assemblies in intended manufacturing process to assure that assembly, function and aesthetical properties comply with the requirements set. In non-rigid variation simulation, components or sub assemblies can deform during assembly. To simulate non-rigid variation the Method of Influence Coefficient (MIC) is typically used. Solving the necessary sensitivity matrices used by MIC is time consuming. In this article we will apply the Sherman-Morrison and Woodbury formula (SMW) for updating the sensitivity response in the different assembly steps. It is shown that SMW can lead to substantial saving in computation time, when compared to the standard MIC.