The optical properties of an exciton trapped by an ionized donor in an ellipsoidal quantum dot (QD) with both oblate and prolate shapes under applied electric field and hydrostatic pressure have been studied. We have calculated the linear and third-order nonlinear absorption coefficients (ACs) and refractive index changes (RICs) by using a variational method within the perturbation theory. The results show that the QD shape and size have a significant influence on the positions and magnitudes of the peaks of the (ACs) and RICs, moreover, the influence of hydrostatic pressure and electric field under different QD shape is also different.