Chemical reactions on the surface or throughout a thermoplastic fiber present an interesting and challenging reaction engineering problem. This paper presents the design and implementation of a modular multiphase continuous stirred tank reactor for the sulfonation of polyethylene fibers. Polyethylene fiber tows, composed of 1000-6000 filaments, are sulfonated in a series of stirred tank reactors. Fundamental reaction engineering principles are applied to address common batch-to-continuous reactor challenges, such as heat and mass transfer, material balances, and reaction kinetics. The introduction of polymer fibers to a continuous process also requires the solution of practical problems associated with fiber processing. Additional considerations are introduced for designing a reactor system for continuous processing of fiber using liquid with a batch reactor or CSTR contacting pattern in each vessel and containing the effluent gaseous reaction byproducts in a controlled vent stream. The overall sulfonation reaction stoichiometry was determined such that approximate to 1 mol of SO3 reacts per mol of CH2 fed. Additionally, carbon sulfonation selectivity was determined to be 95-99%, depending on the sulfonation conditions.