Compound eye-inspired imaging devices can find vast applications due to their remarkable imaging characteristics, such as extremely large field of view angle, low aberrations, high acuity to motion, and infinite depth of field. Recently, researchers have successfully developed a digital camera that resembles the structure and functions of apposition compound eyes of arthropod, by combining an elastic array of microlenses with a stretchable array of photodetectors in their planar form and then transforming into a hemispherical shape. Designing an elastomeric microlens array that can be mechanically stretched to very large extent without deteriorating the optical performance is critical to this development. In this study, mechanics and optics of the stretchable microlens array, in which each hemispherical microlens sits on top of a supporting post connected to a base membrane, are studied. The results show that proper designs of the microlenses, supporting posts and base membrane are critically important to meet both mechanical and optical requirements simultaneously. This study can have important implications in not only the design of artificial compound eye cameras, but also other developments that require stretchable optical elements.