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Abstract Bacterial biofilms are highly abundant 3D living materials capable of performing complex biomechanical and biochemical functions, including programmable growth, self‐repair, filtration, and bioproduction. Methods to measure internal mechanical properties of biofilms in vivo with spatial resolution on the cellular scale have been lacking. Here, thousands of cells are tracked inside living 3D biofilms of the bacteriumVibrio choleraeduring and after the application of shear stress, for a wide range of stress amplitudes, periods, and biofilm sizes, which revealed anisotropic elastic and plastic responses of both cell displacements and cell reorientations. Using cellular tracking to infer parameters of a general mechanical model, spatially‐resolved measurements of the elastic modulus inside the biofilm are obtained, which correlate with the spatial distribution of the polysaccharides within the biofilm matrix. The noninvasive microrheology and force‐inference approach introduced here provides a general framework for studying mechanical properties with high spatial resolution in living materials.