We examine the magnetostriction in amorphous SmCo thin films with a composition in the range 4-27 at.% Sm. The magnetostriction increases significantly with increasing Sm content but is small compared to terbium-based ferromagnetic compounds, despite the large imprinted anisotropy. The magnetostriction and anisotropy both increase approximately linearly as the temperature is reduced. The magnetoelastic energy is found to be far smaller than the anisotropy energy so the magnetoelastic atomic displacements during growth cannot be the origin of the imprinted anisotropy. The anisotropy is only slightly altered by the application of large tensile stresses, indicating that the local strain fields involved in magnetostriction are not equivalent to the global strain produced by mechanical bending.