Mechanosensing of the mechanical microenvironment by cells regulates cell phenotype and function. The nucleus is critical in mechanosensing, as it transmits external forces from the cellular microenvironment to the nuclear envelope housing chromatin. This study aims to elucidate how mechanical confinement affects nuclear deformation within several cell types, and to determine the role of cytoskeletal elements in controlling nuclear deformation. Human cancer cells (MDA-MB-231), human mesenchymal stem cells (MSCs), and mouse fibroblasts (L929) were seeded within polydimethylsiloxane (PDMS) microfluidic devices containing microchannels of varying cross-sectional areas, and nuclear morphology and volume were quantified via image processing of fluorescent cell nuclei. We found that the nuclear major axis length remained fairly constant with increasing confinement in MSCs and MDA-MB-231 cells, but increased with increasing confinement in L929 cells. Nuclear volume of L929 cells and MSCs decreased in the most confining channels. However, L929 nuclei were much more isotropic in unconfined channels than MSC nuclei. When microtubule polymerization or myosin II contractility was inhibited, nuclear deformation was altered only in MSCs in wide channels. This work informs our understanding of nuclear mechanics in physiologically relevant spaces, and suggests diverging roles of the cytoskeleton in regulating nuclear deformation in different cell types.