The mechanism of the initial stage of the ozonolysis of a series of olefins and trans-1,3-butadoiene has been investigated by the B3LYP density functional theory (DFT) method, B2PLYP double hybrid method based on DFT and the MP2 approximation, and CCSD coupled cluster method. Two possible butadiene and olefin ozonolysis mechanisms are considered: concerted 1,3-cycloaddition, which yields a primary ozonide (Criegee mechanism) and stepwise ozone addition via a biradical transition state (DeMore mechanism). The geometries of the initial and transition states and the energies of the elementary steps of the reaction have been determined. The geometric structures of the stationary states determining the rate constant of the reaction have been completely optimized using the above methods and the aug-cc-pVDZ basis set. The rate constants for both reaction pathways have been calculated. For butadiene, the contribution from nonconcerted addition can reaches 25%. According to the MRMP2 method, the overall rate constant (which includes both reaction pathways) is 1778 L mol–1 s–1; according to B2PLYP, 1640 L mol–1 s–1; according to CCSD, 1424 L mol–1 s–1 (aug-cc-pVDZ basis set). These results are in good agreement with experimental data (k = 3 × 103 L mol–1 s–1 and with earlier calculations. The data calculated for olefins are also in agreement with experimental data.