NEED—The effect of dimensional variability of sheet thickness (tolerance) and tool misalignment is poorly understood for the clinching process. Finite element analysis (FEA) is valuable but requires a lot of and is difficult to verify in this situation due to the asymmetrical geometry and nonlinear plasticity. OBJECTIVE—The objective of this work was to determine the effect of thickness tolerance, tool misalignment and sheet placement (top vs. bottom) in the clinching process, by use of analogue modelling with plasticine. METHOD—Experiments used a scaled-up punch and die, with plasticine as the analogue. Thickness tolerances were represented by sheet thicknesses of 11 and 7 mm, 12 and 8 mm, 8 and 12 mm and 13 and 9 mm for upper and lower sheets, respectively. Two types of lubricant were tested between sheets: glycerine and silicone oil. Angular variability was also introduced. Measured parameters were interlock (also called undercut) and neck thickness. Analogue results for deformation were compared with microscopy of metal clinching. FINDINGS—The results reveal that the multiscale analogue model is an efficient tool for studying the effect of dimensional deviation on a clinch joint. Thickness tolerance showed a critical relationship with interlock, namely a reduction to about half that of the nominal, for both maximum and least material conditions. Increased angular misalignment also reduced the interlock. Compared with glycerine, silicone oil tests showed reduced interlock, possibly the result of a lower coefficient of friction. ORIGINALITY—This work demonstrates the usefulness of analogue modelling for exploring process variability in clinching. The results also show that significant effects for sheet placement are ductility, lubricant (friction), thickness of samples and tool misalignment.