We have investigated the possibility of using transparent stretchable diffraction gratings for spectrometric applications. The gratings were fabricated by replication of a triangular-groove master into a transparent viscoelastic. The sample length, and hence the spatial period, can be reversibly changed by mechanical stretching. When used in a monochromator with two slits, the stretchable grating permits scanning the spectral components over the output slit, converting the monochromator into a scanning spectrometer. The spectral resolution of such a spectrometer was found to be limited mainly by the wave-front aberrations due to the grating deformation. A model relating the deformation-induced aberrations in different diffraction orders is presented. In the experiments, a 12-mm long viscoelastic grating with a spatial frequency of 600 line pairs/mm provided a full-width at half-maximum resolution of up to ~1.2 nm in the 580-680 nm spectral range when slowly stretched by a micrometer screw and ~3 nm when repeatedly stretched by a voice coil at 15 Hz. Comparison of aberrations in transmitted and diffracted beams measured by a Shack- Hartmann wave-front sensor showed that astigmatisms caused by stretch-dependent wedge deformation are the main factors limiting the resolution of the viscoelastic-grating-based spectrometer.