The theoretical model, based on the many-band approach, is proposed for the strongly localized donor states in GaAs. The pressure coefficients for the states of Α1 and Τ2 symmetry have been calculated for the donors at the anioii and cation sites. The obtained results show that these pressure coefficients are different from the conduction-band pressure coefficients and are dependent on the lattice site occupied by the impurity as well as on the symmetry of the donor states.PACS numbers: 71.55.-iIn GaAs, the substitutional donor impurities of groups IV and VI can form weakly localized hydrogen-like states as well as strongly localized states. Both the types of donor states can yield energy levels in the gap. Under hydrostatic pressure, the hydrogen-like energy levels change according to the associated conduction-band minimum, whereas the energy levels of the strongly localized states are resonant with the conduction band at the ambient pressure and enter the gap at high pressure. The results of experiments [1][2][3][4] for the strongly localized donor states in GaAs under hydrostatic pressure have been interpreted in different manners. Liu et al. [1] suggest that all strongly localized donor states possess comparable pressure coefficients (about 1 meV/kbar with respect to the valence-band maximum). Dmochowski et al. [2][3][4] argue that the pressure coefficients for the group-IV donors (Si, Ge, Sn) take on the values about 2 meV/kbar, but for the group-VI donors (S, Se) are close to zero. The assignment of symmetry to these states is also not evident. On the one hand, all these states are interpreted as the states of Α 1 symmetry [2-4], on the other hand, the states of Τ2 symmetry cannot be excluded [5]. For the Ge donor, the anticrossing, observed in Ref. [6] under high hydrostatic pressure, between the energy levels of the hydrogen-like 1s state and the strongly localized donor state permits us to assign the Α 1 symmetry to this state.The pressure dependence of the donor states was the subject of few theoretical papers (e.g. [5,7,8]). However, the applied methods are useful either for hydrogen-like donors [5] or for the impurities with deep energy levels [7,8]. The donor levels in GaAs, although associated with the donor states of strong localization, are close to the conduction-band minimum. Therefore, we are dealing with the shallow energy levels both for the weakly and strongly localized donor (671)