Fatty acid methyl esters are extensively used compounds in the industry, but they are perhaps most widely known for their application as biodiesel. In this study, we propose the rotor–stator spinning disc reactor (RS-SDR) as an intensified reactor for the production of fatty acid methyl esters. The RS-SDR relies on the generation of high shear forces in the small gap of a disc, rotating at high speeds, and a stationary wall, to improve on mass and heat transfer rates. Here, we have illustrated the benefits of mass transfer intensification for this reaction by performing the homogeneous base-catalyzed reaction in both a single-stage and a scaled-up multistage RS-SDR. A high level of productivity could be obtained in the multistage reactor (7.78 × 103 mol mR –3 min–1 at a conversion of 82%). Furthermore, we also performed a heterogeneous transesterification reaction with calcined sodium silicate as a slurry catalyst. We were able to obtain a productivity of 214 mol mR –3 min–1 in the RS-SDR (72% conversion, with a residence time of 8 min). In comparison, the batch heterogeneous system had 47% conversion during the same time period of operation. The high slurry concentrations of up to 20 wt % (based on oil weight fraction) did not lead to clogging or fouling in the reactor. These results demonstrate the potential of the RS-SDR for the transesterification reaction.