© The Author(s) 2018. Mechanically stretchable photonics provides a new geometric degree of freedom for photonic system design and foresees applications ranging from artificial skins to soft wearable electronics. Here we describe the design and experimental realization of the first single-mode stretchable photonic devices. These devices, made of chalcogenide glass and epoxy polymer materials, are monolithically integrated on elastomer substrates. To impart mechanical stretching capability to devices built using these intrinsically brittle materials, our design strategy involves local substrate stiffening to minimize shape deformation of critical photonic components, and interconnecting optical waveguides assuming a meandering Euler spiral geometry to mitigate radiative optical loss. Devices fabricated following such design can sustain 41% nominal tensile strain and 3000 stretching cycles without measurable degradation in optical performance. In addition, we present a rigorous analytical model to quantitatively predict stress-optical coupling behavior in waveguide devices of arbitrary geometry without using a single fitting parameter.