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Mechanical characterization of suspended cells by constriction-based microfluidic devices has currently various limitations related to the available analysis models. In this work, we propose a new methodology to analyze the experiments. This approach is based on numerical simulations to describe fluid forces and cell deformation and on an extension of the quasi-linear viscoelasticity theory developed by Fung. The cells are considered visco-hyperelastic, homogeneous, and isotropic. The approach allows for assessing the mechanical parameters of individual cells, which is not possible using previous approaches, notably increasing the power of the constriction-based microfluidic technique. A practical procedure to compute mechanical parameters is proposed and demonstrated by analyzing experiments with suspended cells. The methodology developed in this work provides a convenient tool to overcome critical limitations of the state of the art and to leverage the potential of these microfluidic devices. [Display omitted] • Development of a time-efficient methodology to mechanical characterize individual cells. • Successfully simulated fluid forces and cell squeezing. • A novel heuristic approach, based on Fung's quasi-linear viscoelasticity theory, is proposed. • Demonstrated in an experimental study on the effect of osmolarity on cell deformability using the new mechanical approach. [ABSTRACT FROM AUTHOR]