The pressure-dependent behavior of quasi-local impurity states (QIS) induced by shallow impurity centers in uniaxially stressed p-Ge is described theoretically within screened Coulomb potential model. Dependences of energy position and broadening (lifetime) of QIS on pressure are calculated. They differ fundamentally from the results obtained within a short- range potential model. The wave functions of QIS are built. Perturbation of free hole wave function by the potential of a shallow acceptor is obtained analytically. Effective cross- section of impurity scattering of holes with QIS existing in valence band is calculated. Scattering cross-section dependence upon hole energy has a resonant character. The increase of pressure involves a decrease of cross-section values in the resonance region. Anisotropy of scattering cross-section is explained by anisotropy of free hole wave function perturbation in momentum space.