Substrate utilization by steady state biofilms was described using Monod-type biological kinetics and numerical simulations based on mass transport by molecular diffusion. Substrate concentrations were assumed to vary in flow direction and normal to it. Computer techniques were developed for the numerical evaluation of the normalized biofilm mathematical model. A second-order partial differential equation describing the mechanism of dispersion phenomena inside the liquid layer was then solved to determine the mass transfer coefficient. The application of the theory to experimental results reported in the literature was also demonstrated using the values of mass transfer coefficients obtained and the computer programs developed.