The esterification of the maleic anhydride residue (MA) in a hydrogenated styrene-butadiene-styrene block copolymer (SEBS-g-MA) with a polycaprolactone diol (PCL) was carried out in a melt. Experiments in static melts found that the reaction had an induction period followed by a rapid consumption of the reactants. The gel content accumulation was found synchronous to the consumption of the acidic groups during the reaction process, indicating that the crosslinking between the copolymer molecules prevailed over the esterification of the pendant acid group generated by the ring opening of the MA residue. The reaction rate was strongly affected by both the intensity and the pattern of flow. The reaction rate increased as the flow intensity increased. A back-and-forth shear was more effective in promoting the reaction rate than a one-way shear. This reaction rate enhancement is due to the increase in the interfacial area and concentration gradient caused by the breakup of the dispersed droplets in the melt.