Mesenchymal stem cells can sense and respond to substrate stiffness and topography, which modulates their differentiation into special cell lineages. Vascular cells reside in an elastic extracellular environment and are subjected to normal as well as shear forces. Polyurethane (PU), a synthetic elastomer, is investigated in this study for its potential to promote the attachment and migration of Wharton’s jelly mesenchymal stem cells (WJMSCs). A nanocomposite of PU containing gold nanoparticles (PU-Au) with distinct phase separation on the nanometer scale is also tested because it provides better mechanical/topographical cues compared to those of pristine PU. PU-Au up-regulates the protein expression of focal adhesion kinase (FAK)/Rho-GTPase/matrix metalloproteinase-9 in WJMSCs upon the stimulation of vascular endothelial growth factor (VEGF) and stromal-derived factor-1 (SDF-1). Furthermore, PU-Au improves the attachment and migration of WJMSCs and increases the expression levels of cell surface markers such as CXCR4 and a5p3 integrin after VEGF and SDF-1 stimulation. Collectively, these results suggest that elastic nanocomposites such as PU-Au may enhance WJMSC migration in response to tissue and blood vessel injury, which may in turn contribute to neovascularization in a vascular lesion.