The ability of a cell to regulate its mechanical properties is central to its function. Emerging evidence suggests that interactions between the cell nucleus and cytoskeleton influence cell mechanics through poorly understood mechanisms. Here we conduct quantitative confocal imaging to show that the loss of A-type lamins tends to increase nuclear and cellular volume while the loss of B-type lamins behaves in the opposite manner. We use fluorescence recovery after photobleaching, atomic force microscopy, optical tweezer microrheology, and traction force microscopy to demonstrate that A-type lamins engage with both F-actin and vimentin intermediate filaments (VIFs) through the linker of nucleoskeleton and cytoskeleton (LINC) complexes to modulate cortical and cytoplasmic stiffness as well as cellular contractility in mouse embryonic fibroblasts (MEFs). In contrast, we show that B-type lamins predominantly interact with VIFs through LINC complexes to regulate cytoplasmic stiffness and contractility. We then propose a physical model mediated by the lamin–LINC complex that explains these distinct mechanical phenotypes (mechanophenotypes). To verify this model, we use dominant negative constructs and RNA interference to disrupt the LINC complexes that facilitate the interaction of the nucleus with the F-actin and VIF cytoskeletons and show that the loss of these elements results in mechanophenotypes like those observed in MEFs that lack A- or B-type lamin isoforms. Finally, we demonstrate that the loss of each lamin isoform softens the cell nucleus and enhances constricted cell migration but in turn increases migration-induced DNA damage. Together, our findings uncover distinctive roles for each of the four major lamin isoforms in maintaining nucleocytoskeletal interactions and cellular mechanics.