<p> A living cell is a complex soft matter system far from equilibrium. While its components have definite mechanical properties such as stiffness and viscosity, cells consume energy to generate force and exhibit adaptation by modulating their mechanical properties through regulatory pathways. In this dissertation, we explore cell mechanics by stretching single fibroblast cells and simultaneously measuring their traction stresses. Upon stretch, there is a sudden, drastic increase in traction stresses, often followed by a relaxation over a time scale of about 1 minute. Upon release of stretch, traction stresses initially drop and often recover on a similar time scale of about 1 minute. We show that a minimal active linear viscoelastic model captures essential features of cell response to stretch. This model is most successful in describing the response of cells within the first 30 seconds of stretch. While perturbations of myosin and vinculin change quiescent traction stresses, they surprisingly have no significant impact on the stiffness or viscoelastic timescale of the cells. On longer time scales, cells may show an adaptive response to stretch that contradicts the minimal mechanical model. The probability of an adaptive response is significantly reduced by myosin de-activation and vinculin knockout. Therefore, we find that while vinculin and myosin are not important in determining passive mechanical properties of cells, such as stiffness and viscosity, they play a significant role in the adaptive mechanisms of cell response to stretch. To perform this work, we have built a novel micro stretching device compatible with live cell microscopy and developed a computational tool to analyze data from large traction stresses. Therefore, this dissertation's contribution is two-fold: (1) a novel experimental approach to explore the mechanics of living cells, and (2) a new model and framework for understanding the mechanical response of cells to stretch.</p>