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Precision engineering has been used in the macroworld and in the microscale only with rigid materials. Soft flexible materials commonly used for microfluidics and other bio-MEMS applications have not been aligned with elastic averaging. We report the use of complementary raised and recessed circular features to align polymer layers and demonstrate alignment accuracy and repeatability. The alignment is accomplished in a Petri dish with a thin layer of liquid between the two surfaces of micromolded elastomeric polymer sheets. The layers are aligned with simple hand-eye manipulation. We test circular geometries of varying diameters, obtaining accuracy and repeatability values in the range of 1-3 mum across thin polymer sheets molded from silicon masters. This is a significant improvement over existing manual, moving stage, and self-alignment techniques and a novel proof of concept that paves the way for complex 3-D polymer constructs.