We develop a model of an epitaxial self-organized InGaAs quantum dot buried in GaAs, which takes into account experimentally determined indium distribution inside the QD, its geometry and crystallography. The problem of solid mechanics was solved to determine the stress-strain field. Then, the parameters of the electron and hole ground states were evaluated by solving the problem of the quantum mechanics on the same mesh. The results of calculations appeared to be reasonably well consistent with experimentally recorded optical emission spectra for the QDs in the same sample. The experimentally-verified modeling reveals a bagel-like shape of the hole wave function at the ground state, which should considerably impact the optical and magnetic properties of the QDs. Such shape of the wave function is beyond the predictions of simplified models with uniform indium distribution