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Aortic Smooth Muscle Cells (SMCs) play a vital role in maintaining homeostasis in the aorta by sensing and responding to mechanical stimuli. However, the mechanisms that underlie the ability of SMCs to sense and respond to stiffness change in their environment are still partially unclear. In this study, we focus on the role of acto-myosin contractility in stiffness sensing and introduce a novel continuum mechanics approach based on the principles of thermal strains. Each stress fiber satisfies a universal stress-strain relationship driven by a Young’s modulus, a contraction coefficient scaling the fictitious thermal strain, a maximum contraction stress and a softening parameter describing the sliding effects between actin and myosin filaments. To account for the inherent variability of cellular responses, large populations of SMCs are modeled with the finite-element method, each cell having a random number and a random arrangement of stress fibers. Moreover, the level of myosin activation in each stress fiber satisfies a Weibull probability density function. Model predictions are compared to traction force measurements on different SMC lineages. It is demonstrated that the model not only predicts well the effects of substrate stiffness on cellular traction, but it can also successfully approximate the statistical variations of cellular tractions induced by intercellular variability. Finally, stresses in the nuclear envelope and in the nucleus are computed with the model, showing that the variations of cytoskeletal forces induced by substrate stiffness directly induce deformations of the nucleus which can potentially alter gene expression. The predictability of the model combined to its relative simplicity are promising assets for further investigation of stiffness sensing in 3D environments. Eventually, this could contribute to decipher the effects of mechanosensitivity impairment, which are known to be at the root of aortic aneurysms.