In this contribution, we present a constitutive model to describe the mechanical behaviour of microbial biofilms based on classical approaches in the continuum theory of polymer networks. Although the model is particularly developed for the well-studied biofilms formed by mucoid Pseudomonas aeruginosa strains, it could easily be adapted to other biofilms. The basic assumption behind the model is that the network of extracellular polymeric substances can be described as a superposition of worm-like chain networks, each connected by transient junctions of a certain lifetime. Several models that were applied to biofilms previously are included in the presented approach as special cases, and for small shear strains, the governing equations are those of four parallel Maxwell elements. Rheological data given in the literature are very adequately captured by the proposed model, and the simulated response for a series of compression tests at large strains is in good qualitative agreement with reported experimental behavior.