Affinity separations rely on the highly specific binding between a protein in solution and an immobilized ligand to achieve a high degree of protein purification. A mathematical model including convection, diffusion, and rate kinetics is formulated to analyze the design and operation of affinity membrane bioseparations. The model equations are solved by orthogonal collocation method. Danckwerts' boundary conditions are used. The results obtained from model simulation show that the breakthrough of the protein is significantly influenced by Peclet number, feed protein concentration, Ligand number, Damkohler number, membrane thickness, and flow rate. Breakthrough profiles are quantitatively discussed in terms of protein recovery efficiency, ligand utilization efficiency, thickness of unused membrane, and width of the mass transfer zone.