The measurement of cell stiffness is an important part of biological research with diverse applications in biology, biotechnology and medicine. Real-time deformability cytometry (RT-DC) is a new method to probe cell stiffness at high throughput by flushing cells through a microfluidic channel where cell deformation provides an indicator for cell stiffness (Otto et al. Real-time deformability cytometry: on-the-fly cell 725 mechanical phenotyping. Nat. Methods 2015, 12, 199-202). Here, we propose a full numerical model for single cells in a flow channel to quantitatively relate cell deformation to mechanical parameters. Thereby the cell is modeled as a viscoelastic material surrounded by a thin shell cortex, subject to bending stiffness and cortical surface tension. For small deformations our results show good agreement with a previously developed analytical model that neglects the influence of cell deformation on the fluid flow (Mietke et al. Extracting Cell Stiffness from Real-Time Deformability Cytometry: 728 Theory and Experiment. Biophys. J. 2015, 109, 2023-2036). Including linear elasticity as well as neo-Hookean hyperelasticity, our model is valid in a wide range of cell deformations and allows to extract cell stiffness for largely deformed cells. We introduce a new measure for cell deformation that is capable to distinguish between deformation effects stemming from cell cortex and cell bulk elasticity. Finally, we demonstrate the potential of the method to simultaneously quantify multiple mechanical cell parameters by RT-DC.