In the shipbuilding industry, steel plates are assembled and joined to construct a block, and dozens of blocks are erected to build a ship. The major joining process used to assemble the steel plates is welding. Because the welding process causes strong non-uniform heating of the parts being joined, the local heating and subsequent cooling of welded pieces induce volumetric changes, producing transient and residual stresses as well as plastic deformation. This welding distortion is the main factor causing geometrical imperfections in the steel plate assembly process. These non-nominally shaped parts need to be clamped before the following joining process, which in turn causes pre-stress in the parts being joined. The pre-stresses due to welding and clamping significantly affect the subsequent welding processes. This paper proposes a variation simulation model of compliant assemblies to analyze the propagation of geometrical variations through multiple assembly stages, including the welding distortion under the effect of the pre-stress state. This research extends the mechanical variation simulation model to include the effects of clamping stresses by expressing the pre-stress terms in the form of an additional stiffness matrix. The result helps in confirming the effect of the pre-stress state on the subsequent welding distortion in the multi-stage assembly process. The proposed model can be used to predict the propagation of assembly variation in steel plate assemblies considering the pre-stress effect and welding distortion.