We characterise for the first time a surface instability that occurs when a yield stress fluid is subject to uniaxial compression. We describe experiments using a pre-stretched elastic sheet which, upon controlled release, uniaxially compresses a layer of Petroleum Jelly creating surface undulations perpendicular to the direction of compression. We measure experimentally the amplitude and wavelength of the surface undulations, and their dependence on the thickness of the material and the Bingham number, the non-dimensional yield stress. Results show that the amplitude of the undulations depends linearly on the Bingham number, whereas the wavelength scales with the initial thickness of the compressed layer. These experiments enhance our understanding of surface instabilities in related systems, such as recent experiments scraping a thin layer of a viscoplastic fluid. Characterising these surface undulations is integral for geophysical applications in understanding topographic features in accretionary wedges.