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New advances in the mathematical modeling of the bulk continuous high‐impact polystyrene (HIPS) process are presented. The model consists of three modules that allow the simulation of: (1) a polymerization reactor train, (2) a devolatilization (DV) stage, and (3) structure–properties relationships. The model is based on a kinetic mechanism that includes thermal initiation, chemical initiation by sequential decomposition of a multifunctional initiator, propagation, transfer to monomer, transfer to rubber, termination by combination and re‐initiation, as well as high temperature crosslinking and oligomer generation reactions. The present model is comprehensive from a kinetic perspective, since it can be used to simulate a HIPS process using initiators of any functionality and structure. The model is adjusted and validated using previously unpublished experimental data for bulk continuous HIPS polymerization in a pilot‐scale plant. The experimental work includes a series of polymerizations using three different multifunctional initiators: (1) luperox‐331 M80 (L331), (2) pinacolone diperoxide, and (3) diethyl ketone triperoxide. The pilot plant comprised the main stages of an industrial HIPS process: prepolymerization, finishing and DV. Theoretical results show a good agreement with the experimental measurements. POLYM. ENG. SCI., 59:E231–E246, 2019. © 2018 Society of Plastics Engineers [ABSTRACT FROM AUTHOR]