Biofilms are complex colonies of bacteria that grow when in contact with a wall, and this, often in the presence of a water flow. I investigate biofilm colony growth using a two-dimensional lattice Monte-Carlo simulation based on the bond-fluctuation algorithm (BFA). A distinguishing characteristic of biofilms is the extracellular polymeric substance (EPS) --- this is the slime that often builds up on the walls of water conduits. In our simulations, the synthesis and physical properties of the EPS (into which the bacterial cells are embedded) are explicitly taken into account. Cells are modeled as autonomous closed loops with well-defined mechanical and biological properties, while the EPS is modeled as flexible polymeric chain synthesized by the cells during their growth. By tuning the structural, energetic, biological, and morphologic parameters of the model, the individual cell shape as well as the overall growth and maturation of biofilm colonies (including colonies with multiple species) can be controlled.