Engineered living materials (ELMs) constitute a novel class of functional materials that contain living organisms. The mechanical properties of many such systems are dominated by the polymeric matrices used to encapsulate the cellular components of the material, making it hard to tune the mechanical behavior through genetic manipulation. To address this issue, we have developed living materials in which mechanical properties are controlled by the cell-surface display of engineered proteins. Here, we show that engineered Esherichia coli cells outfitted with surface-displayed elastin-like proteins (ELPs, designated E6) grow into soft, cohesive bacterial films with biaxial moduli around 14 kPa. When subjected to bulge-testing, such films yielded at strains of approximately 10%. Introduction of a single cysteine residue near the exposed N-terminus of the ELP (to afford a protein designated CE6) increases the film modulus 3-fold to 44 kPa and eliminates the yielding behavior. When subjected to oscillatory stress, films prepared from E. coli strains bearing CE6 exhibit modest hysteresis and full strain recovery; in E6 films much more significant hysteresis and substantial plastic deformation are observed. CE6 films heal autonomously after damage, with the biaxial modulus fully restored after a few hours. This work establishes an approach to living materials with genetically programmable mechanical properties and a capacity for self-healing. Such materials may find application in biomanufacturing, biosensing, and bioremediation.