Flexibility of assembly systems is crucial to maintaining the competitiveness in the rapidly changing market. In this paper, a novel flexible fixturing system for sheet metal part assembly is presented, which utilizes parallel robots as reconfigurable fixture elements. The method of influence coefficients, combined with finite element analysis and screw theory, is used to analyze the variations in sheet metal assembly. In the analysis of assembly variations, a total of six variations involved in prewelding, underwelding, and afterwelding process are intensively considered. Screw theory is employed to model the kinematic and constraint features corresponding to the fixturing schemes. A robust fixture layout design model is developed based on the Lagrangian conditional extremum method. A case study illustrates that the robust optimal methodology and an optimal fixture layout scheme with less sensitivity can be obtained.