Despite their large lattice mismatch of 18 %, the lattices of Bi(111) and Si(001) fit surprisingly well. A remaining compressive strain in the Bi film of 2.3 % along the direction is accommodated by the formation of a periodic array of edge-type misfit dislocations confined to the interface. The strain fields surrounding each dislocation interact with each other, producing a quasi-periodic nanopattern of grating-like periodic height undulations on the surface. The separation and the amplitude of the height undulations have been derived by spot profile analyzing LEED and STM surface height profiles. The observed undulations agree well with elasticity theory.