We present a three dimensional (3D) microenvironment for on-chip cell culture, with engineered geometrical and mechanical properties. The device, named mu-flower, is based on micorfabricated cantilever beams bent out of plane by the intrinsic stresses of a bilayer structure. The use of Ti-SiO2 bilayers with various thicknesses allows spanning a large range of rigidities while keeping the size nearly constant. The geometrical and mechanical properties of the devices are thus decoupled, and the degrees of stiffness of several physiological tissues are matched. These characteristics make mu-flowers a microfabricated cell-culture substrate designed to mimic essential physical properties of the in vivo environment (dimensionality, shape and rigidity) in a precisely controlled way, at the single-cell scale, and with a high degree of parallelization.