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The cell biomechanical properties play a key role in the determination of the changes during the essential cellular functions, such as contraction, growth, and migration. Recent advances in nano-technologies have enabled the development of new experimental and modeling approaches to study cell biomechanics, with a level of insights and reliability that were not possible in the past. The use of atomic force microscopy (AFM) for force spectroscopy allows nanoscale mapping of the cell topography and mechanical properties under, nearly physiological conditions. A proper evaluation process of such data is an essential factor to obtain accurate values of the cell elastic properties (primarily Young's modulus). Several numerical models were published in the literature, describing the depth sensing indentation as interaction process between the elastic surface and indenting probe. However, many studies are still relying on the nowadays outdated Hertzian model from the nineteenth century, or its modification by Sneddon. The lack of comparison between the Hertz/Sneddon model with their modern modifications blocks the development of advanced analysis software and further progress of AFM promising technology into biological sciences. In this work, we applied a rationalized use of mechanical models for advanced postprocessing and interpretation of AFM data. We investigated the effect of the mechanical model choice on the final evaluation of cellular elasticity. We then selected samples subjected to different physicochemical modulators, to show how a critical use of AFM data handling can provide more information than simple elastic modulus estimation. Our contribution is intended as a methodological discussion of the limitations and benefits of AFM-based advanced mechanical analysis, to refine the quantification of cellular elastic properties and its correlation to undergoing cellular processes in vitro.