The ethylene/1-butene copolymerization using constrained geometry catalyst CpSiH 2 -NH-TiCl 2 (CGC) was investigated by the density functional theory and molecular dynamics. Structures and energetics of reactants, π-complexes, transition states, and products during insertion of ethylene and 1-butene monomers into the catalytic reactive site of the CGC were investigated by the density functional theory (DFT) using the software Dmol 3 , while dynamics of atoms during copolymerization process was investigated by classical molecular dynamics (MD) using the New-Ryudo-CR program. The calculated results were compared with the available experimental and theoretical ones. It was found that the ethylene insertion into Ti-Me active species is energetically more favorable than the butene one and the 2,1-butene insertion is more favorable than 1,2-butene one. Once the initial ethylene insertion has taken place, the further ethylene insertion occurring with a less energy barrier, in good agreement with experimental findings.