The mechanisms of the initial step in chemical reaction between ozone and ethylene were studied by multireference perturbation theory methods (MRMP2, CASPT2, NEVPT2, and CIPT2) and density functional theory (OPW91, OPBE, and OTPSS functionals). Two possible reaction channels were considered: concerted addition through the symmetric transition state (Criegee mechanism) and stepwise addition by the biradical mechanism (DeMore mechanism). Predicted structures of intermediates and transition states, the energies of elementary steps, and activation barriers were reported. For the rate-determining steps of both mechanisms, the full geometry optimization of stationary points was performed at the CASPT2/cc-pVDZ theory level, and the potential energy surface profiles were constructed at the MRMP2/cc-pVTZ, NEVPT2/cc-pVDZ, and CIPT2/cc-pVDZ theory levels. The rate constants and their ratio for reaction channels calculated for both mechanisms demonstrate that the Criegee mechanism is predominant for this reaction. These results are also in agreement with the experimental data and previous computational results. The structure of DeMore prereactive complex is reported here for the first time at the CCSD(T)/cc-pVTZ and CASPT2/cc-pVDZ levels. Relative stability of the complexes and activation energies were refined by single-point energy calculations at the CCSD(T)-F12/VTZ-F12 level. The IR shifts of ozone bands due to formation of complexes are presented and discussed.