Machining accuracy and tolerances achieved using modular fixtures are inferior to those achieved using dedicated fixtures. This is mainly because they are built by assembling individual components, which results in positional and dimensional inaccuracies due to their manufacturing tolerances being added up. It is therefore important to plan the fixture configuration such that the effect of fixture elements tolerances is least at the critical machining regions. In this work, an attempt is made to minimize the deviation at the machining zone due to the variation in size and thereby selecting the position of locating and supporting elements. The definition of a solid is considered in the most accurate form by taking NURBS-based IGES/STEP part model as input. All feasible (unique and accessible) triplets of locating positions at different locating heights are determined. It is demonstrated that the modular fixture plans can be significantly improved by changing the locating plane height. The fixturing plans are graded using three-dimensional tolerance analysis for a given machining set-up with respect to the deviation at the critical machining features. The most appropriate locating scheme for which the tolerance errors at selected machining zones is minimum is chosen.