Li -sulfur batteries represent a promising class of next -generation batteries with high theoretical gravimetric capacity. Moreover, the absence of scarce elements such as nickel or cobalt makes them a sustainable alternative to Li -ion batteries. However, it is well known that the main problem of Li -sulfur batteries is the so-called polysulfide shuttle, which leads to self -discharge, capacity fading and low coulombic efficiency. In recent years, several mitigation strategies have been developed for Li -sulfur batteries to reduce the polysulfide shuttle effect. One promising approach is to covalently bond the sulfur to a polymer backbone. A well-known class of materials is sulfurized poly(acrylonitrile) (SPAN), for which long cycle life and high specific capacities have been reported. In this work, we present a novel continuum model for SPAN electrodes and demonstrate its application in Li -SPAN batteries. Within our simulation framework we include both red/ox reactions of covalently sulfur on PAN as well as transport and reactions of polysulfides in the solution. By combining simulations and experimental data we analyze the discharge mechanism and provide guidelines for electrode design.