This paper is dedicated to the study on the external and internal mass transfers of glucose for succinic acid fermentation under substrate and product inhibitions using a bioreactor with stirred bed of immobilized Actinobacillus succinogenes cells. By means of the substrate mass balance for a single particle of biocatalysts, considering the kinetic model adapted for both inhibitory effects, specific mathematical models were developed for describing the profiles of the substrate concentration in the outer and inner regions of biocatalysts and for estimating the substrate mass flows in the liquid boundary layer surrounding the particle and inside the particle. The values of the mass flows were significantly influenced by the internal diffusion velocity and rate of the biochemical reaction of substrate consumption. These cumulated influences led to the appearance of a biological inactive region near the particle center, its magnitude varying from 0 to 5.3% of the overall volume of particles.