As a model of olefin polymerization for a heterogeneous Ziegler᎐Natta catalyst, the mechanisms of the insertion of ethylene and propylene into R-Ti-Ž . q Ž . Ž . Cl AlH R s CH , C H are studied by ab initio self-consistent field SCF methods 2 2 2 3 3 7and many-body perturbation theory. The structures of the reactant, the intermediate, the transition state, and the product are optimized by the Hartree᎐Fock molecular orbital calculation level. The reactions are classified into two steps: the first forms of olefin᎐Ti complex, and the second step is the carbon᎐carbon bond formation through the pull᎐push mechanisms. The cocatalysis play a role in facilitating the pull᎐push mechanism with the Al᎐Cl bonds alternation. For the insertion reaction of propylene, the four-type Ž conformations for attacking of propylene two primary forms: methyl-substituted carbon attacks to the carbon side of Ti᎐C bond; two secondary forms: methyl-substituted carbon . attack to Ti atom are studied. For the complex formation, the secondary forms are more stable in energy than the primary forms. For the transition state, the primary forms are more stable in energy than the secondary forms.