A closed‐form solution is presented for the stresses induced in an infinite elastic body by a periodic array of misfitting inclusions. This solution is used to study the mechanical and electronic properties of buried arrays of [11¯0]‐oriented strained quantum wires. A critical mismatch condition along the lines of the Matthews and Blakeslee condition for strained layers is developed and is used to show that quantum wire structures should be extremely stable in the postgrowth processing stages provided that the repeat period of the array is more than four times the dimension of a wire. If the period is more than five times the wire dimension then each member of the array behaves like an isolated wire. It is shown that stability problems for closely spaced arrays may be avoided by choosing the direction in which the wires are periodically distributed to be [001] rather than [110]. The formulas are also used to investigate the difference between the strain‐induced band gap shifts of quantum wires and wells experiencing the same lattice mismatch with the growth substrate. It is found that the dilatation is identical in the two structures so that, in the InGaAs system, wells and wires of the same composition should have very similar band gaps. By contrast, conduction‐band splitting in the GeSi system can give rise to differences of up to 100 meV between the band gaps of the two structures. These results are shown to compare very favorably with experiment. ©1995 American Institute of Physics.