Peculiarities of the etching kinetics and mechanisms for Si and SiO2 in the HBr+Cl-2+O-2 inductively coupled plasma were investigated by analyzing the relationships between etching rates and fluxes of active species. The data on plasma parameters, plasma chemistry, and the steady-state plasma composition were obtained using both Langmuir probe diagnostics and 0-dimensional plasma modeling. It was found that an increase in the Cl-2 mixing ratio and input power causes similar trends in the changes in ion energy flux and halogen atom flux but results in different tendencies for both Si and SiO2 etching rates. It was shown that the influence of input process parameters (HBr/Cl-2 mixing ratio, input power, and bias power) on the Si and SiO2 etching kinetics may be adequately described in terms of the oxygen atom flux-sensitive reaction probability. The latter directly correlates with the oxygen atom flux/ion energy flux ratio.