Biofilms are biological materials composed of microbial communities encased in a self-produced extracellular polymeric substance (EPS). The viscoelastic properties of biofilms are related to the cross-link density in the EPS and ultimately the cohesiveness of biofilms. Accurate measurement of biofilm viscoelastic properties at the mesoscale remains a challenge. Rheological measurements, although being more common, provide only global properties, do not permit in-situ characterization, and are not amenable to complex sample geometries. To address these challenges, our work seeks to develop a nondestructive framework for characterizing biofilm viscoelastic properties using elastic wave propagation measured by the optical coherence elastography technique. The framework holds great potential to elucidate spatially varying mechanical properties and their correlation with sample morphology and composition.