In this paper an analysis of the excitation conditions of mirror waves is d
one, which propagate parallel to an external magnetic field. There are foun
d analytical expressions for the dispersion relations of the waves in case
of different plasma conditions. These relations may be used in future to de
velop the nonlinear theory of mirror waves. In comparison with former analy
tical works, in the study the influence of the magnetic field and finite te
mperatures of the ions parallel to the magnetic field are taken into accoun
t. Application is done for the earth's magnetosheath.