This paper reports the study on the synthesis of poly(epsilon-caprolactone)-PCL by ring-opening polymerization (ROP) of epsilon-caprolactone (CL) monomer with focus on mathematic developing of the growth mechanisms of polymer chain. Kinetics and mathematical modeling of ROP of CL was carried out to replicate the different experimental conditions. The computational results of conversion and molecular weight of the polymer were found to be comparable with the experimental results of nuclear magnetic resonance (NMR) spectroscopy and showed that the polymerization is highly dependent on the moisture (ROH). Moreover, parametric studies have shown how the concentrations of octanoic acid and catalyst affect the conversion and molecular weight of the polymer. The study here presented provides further understanding of synthesis of PCL, reporting mathematical models of PCL synthesis which can be used for predicting the characteristic of this biocompatible and biodegradable polymer.