The detailed mechanobiology of how cells biochemically transduce mechanical signals is reshaping our basic understanding of life and pathology. In particular, Yes Associated Protein (YAP) has emerged as a key mechanosensitive transcriptional factor in diverse organisms, and quite broadly in human development and pathology. In our research, we employ a variety of biophysical approaches to present a comprehensive analysis of the relationship between cell contractility, nuclear deformation, Lamin A localization, and YAP nuclear translocation.  We have found that nuclear deformation from LINC-mediated cytoskeletal contractility or extracellular osmotic forces triggers YAP nuclear localization. By modulating the expression of lamin A and nuclear stiffness, we find that nuclear rigidity modulates deformation-mediated YAP nuclear localization.