A double template-assisted fabrication method for making surface patterns with tunable lattice geometries on a polymer surface is reported. This technique is based on a locally nonuniform strain produced in a double-templated polymer film that has a strong modulation in thickness. It can produce all 2D primitive Bravais lattices as well as chains on the surface of a polymer. The lattice parameters are controllable with nanoprecision by varying the direction and amount of the applied strain.