Membrane chromatography is an emerging bioprocessing technology. This work aimed to determine the cause of pressure rise during the loading phase of a large-scale viral recovery process, through small-scale experimentation. Comparable pressure rise was observed at both small and large scales, using Sartobind® Q anion exchange membranes. By varying low rate and feed concentrations of virus and host cell DNA, a linear relation between Viral Dynamic Dynamic Binding Capacity (DBC) and pressure rise was observed when DNA levels exceeded 1 × 10−8 g/ml. A mathematical model, assuming an uncompetitive interaction between the two species in a representative pore, was developed to predict breakthrough from which DBC and then pressure rise was determined. The results matched experimental data quite well at low to moderate DBC values (ie <8 mg/ml membrane), and can be utilized to anticipate pressure rise when higher DNA levels give rise to problematic levels of pressure rise.