The article presents a mathematical model of biofilm growth for aerobic biodegradation of a toxic carbonaceous substrate. Modelling of biofilm growth has fundamental significance in numerous processes of biotechnology and mathematical modelling of bioreactors. The process following double-substrate kinetics with substrate inhibition proceeding in a biofilm has not been modelled so far by means of cellular automata. Each process in the model proposed, i.e. diffusion of substrates, uptake of substrates, growth and decay of microorganisms and biofilm detachment, is simulated in a discrete manner. It was shown that for flat biofilm of constant thickness, the results of the presented model agree with those of a continuous model. The primary outcome of the study was to propose a mathematical model of biofilm growth; however a considerable amount of focus was also placed on the development of efficient algorithms for its solution. Two parallel algorithms were created, differing in the way computations are distributed. Computer programs were created using OpenMP Application Programming Interface for C ++ programming language. Simulations of biofilm growth were performed on three high-performance computers. Speed-up coefficients of computer programs were compared. Both algorithms enabled a significant reduction of computation time. It is important, inter alia, in modelling and simulation of bioreactor dynamics.