The ability to render objects invisible with a cloak that fits all objects and sizes is a long-standing goal for optical devices. Invisibility devices demonstrated so far typically comprise a rigid structure wrapped around an object to which it is fitted. Here we demonstrate smart metamaterial cloaking, wherein the metamaterial device not only transforms electromagnetic fields to make an object invisible, but also acquires its properties automatically from its own elastic deformation. The demonstrated device is a ground-plane microwave cloak composed of an elastic metamaterial with a broad operational band (10-12 GHz) and nearly lossless electromagnetic properties. The metamaterial is uniform, or perfectly periodic, in its undeformed state and acquires the necessary gradient-index profile, mimicking a quasi-conformal transformation, naturally from a boundary load. This easy-to-fabricate hybrid elasto-electromagnetic metamaterial opens the door to implementations of a variety of transformation optics devices based on quasi-conformal maps.