Molecular sieves, including carbon molecular sieves (CMSs) manufactured from activated carbons, can be variously applied in the purification and separation of gaseous and liquid mixtures and can also serve as catalysts. CMSs are formed by depositing fine particles of carbon on the mouths of pores of such activated carbons. These carbon particles are generated by decomposing a gaseous carbon source. The formation of CMSs proceeds stochastically, which is mainly attributable to the mesoscopic sizes and complex motion of the depositing carbon particles and random distribution of the pores on the activated carbons. In this work, CMS formation is modeled as a pure-birth process with a linear intensity of transition. The resultant model gives rise to the governing equations for the mean and variance. The model is validated by comparing the analytical solutions of these equations with available experimental data. The mean value of the model is in excellent accord with the data. In addition, the kinetic constants resulting from the model have been found to obey the Arrhenius law.