  We report significant deviations from the usual quadratic dependence of the
ground state interband transition energy on applied electric fields in
InAs/GaAs self-assembled quantum dots. In particular, we show that conventional
second-order perturbation theory fails to correctly describe the Stark shift
for electric field below $F = 10$ kV/cm in high dots. Eight-band ${\bf
k}\cdot{\bf p}$ calculations demonstrate this effect is predominantly due to
the three-dimensional strain field distribution which for various dot shapes
and stoichiometric compositions drastically affects the hole ground state. Our
conclusions are supported by two independent experiments.
