A novel biofilm model is described which systemically couples bacteria, extracellular polymeric substances (EPS) and solvent phases in biofilm. This enables the study of contributions of rheology of individual phases to deformation of biofilm in response to fluid flow as well as interactions between different phases. The model, which is based on first and second laws of thermodynamics, is derived using an energetic variational approach and phase-field method. Phase-field coupling is used to model structural changes of a biofilm. A newly developed unconditionally energy-stable numerical splitting scheme is implemented for computing the numerical solution of the model efficiently. Model simulations predict biofilm cohesive failure for the flow velocity between O(10-3) and O(10-2) m s21 which is consistent with experiments. Simulations predict biofilm deformation resulting in the formation of streamers for EPS exhibiting a viscous-dominated mechanical response and the viscosity of EPS being less than O(10) kgm-1 s-1. Higher EPS viscosity provides biofilm with greater resistance to deformation and to removal by the flow. Moreover, simulations show that higher EPS elasticity yields the formation of streamers with complex geometries that aremore prone to detachment. These model predictions are shown to be in qualitative agreement with experimental observations.