The mechanical properties of cells are governed by the cytoskeleton, a dynamic network of actin filaments, intermediate filaments, and microtubules. Understanding the individual and collective mechanical contributions of these three different cytoskeletal elements is essential to elucidate how cells maintain mechanical integrity during deformation. Here we use a custom single-cell rheometer to identify the distinct contributions of actin and vimentin to the viscoelastic and nonlinear elastic response of cells to uniaxial compression. We used mouse embryonic fibroblasts (MEFs) isolated from wild type (WT) and vimentin knockout (vim -/-) mice in combination with chemical treatments to manipulate actin polymerization and contractility. We show through small amplitude oscillatory measurements and strain ramp tests that vimentin, often overlooked in cellular mechanics, plays a role comparable to actin in maintaining cell stiffness and resisting large compressive forces. However, actin appears to be more important than vimentin in determining cellular energy dissipation. Finally we show by comparing wild type and enucleated cells that compression stiffening originates from the actin and vimentin cytoskeleton, while the nucleus appears to play little role in this. Our findings provide insight into how cytoskeletal networks collectively determine the mechanical properties of cells, providing a basis to understand the role of the cytoskeleton in the ability of cells to resist external as well as internal forces.Significance statementA cell’s response to mechanical stress is largely governed by the actin and vimentin cytoskeletal networks, but their relative contribution to cell viscoelasticity and response to large deformations are poorly characterized.We reveal that actin and vimentin networks have an almost equal contribution to cellular stiffness and the cell’s ability to strain-stiffen under uniaxial compression.This work underscores the cytoskeleton’s central role in cellular mechanics and the mechanical synergy between the cytoskeletal networks, providing a framework for understanding how cellular components coordinate to maintain structural integrity and respond to different mechanical environments.