  The influence of various kinds of impurities on the isotope shift exponent
\alpha of high temperature superconductors has been studied. In these materials
the dopant impurities, like Sr in La_{2-x}Sr_xCuO_4, play different role and
usually occupy different sites than impurities like Zn, Fe, Ni {\it etc}
intentionally introduced into the system to study its superconducting
properties.
  In the paper the in-plane and out-of-plane impurities present in layered
superconductors have been considered. They differently affect the
superconducting transition temperature T_c. The relative change of isotope
shift coefficient, however, is an universal function of T_c/T_{c0} (T_{c0}
reffers to impurity free system) {\it i.e.} for angle independent scattering
rate and density of states function it does not depend whether the change of
T_c is due to in- or out-of-plane impurities. The role of the anisotropic
impurity scattering in changing oxygen isotope coefficient of superconductors
with various symmetries of the order parameter is elucidated. The comparison of
the calculated and experimental dependence of \alpha/\alpha_0, where \alpha_0
is the clean system isotope shift coefficient, on T_c/T_{c0} is presented for a
number of cases studied.
  The changes of \alpha calculated within stripe model of superconductivity in
copper oxides resonably well describe the data on
La_{1.8}Sr_{0.2}Cu_{1-x}(Fe,Ni)_xO_4, without any fitting parameters.
