Cost-effective conversion of lignocellulosic biomass to fermentable sugars for renewable fuel production remains a formidable challenge for the economically feasible operation of bio-refineries.  An improved understanding of the conversion reactions and the development of predictive models will help in overcoming this challenge.  In this work, we developed a mechanistically based mathematical model for enzymatic hydrolysis kinetics of cellulose substrates.  The distinct modes of action of the cellulase enzymes on soluble and insoluble substrates are each described by separate rate expressions. Depolymerization of the insoluble substrate by adsorbed enzyme is calculated using distribution kinetics, which tracks the molecular-weight distribution of the cellulose chains, rather than the concentration of individual species, over time.  Using the method-of-moments affords computationally efficient calculations, regardless of the size or polydispersity of the polymer chains.  Competitive product inhibition and the time evolution of enzyme-accessible substrate are also included. Model results throughout enzymatic saccharification are compared to experimental results.  Our model is capable of examining many of the relevant phenomena occurring during enzymatic saccharification, and aims to guide process development and identify optimal process-operating conditions.