We have developed mechanistically based mathematical models for the dilute-acid pretreatment of lignocellulosic biomass, which consider the various physical and chemical changes to the feedstock during pretreatment. Such a model can aid in interpreting experimental results, determining reaction mechanisms, and scale-up of pretreatment processes. The spatial distribution of reactants and products during pretreatment can significantly influence the dynamic-conversion profiles for xylan solubilization and overall xylose yields, especially for high-solids loadings.  A population-balance model, which incorporates the effects of feedstock particle structure, particle-size distribution, and fragmentation, captures many of the relevant changes to the substrate during pretreatment and can potentially help identify the chemical and structural changes that result in high-xylose yields and enhanced-enzymatic digestibility. The effect of incomplete-acid impregnation of biomass particles is also considered.