Force-displacement (F-ZIn recent years interest has increased in the measurement of the viscoelastic properties of soft biological samples motivated by their correlation with disease, differentiation, or cellular transformation [1][2][3][4] . A large variety of methods have been introduced for measuring cellular mechanical properties including micropipette aspiration 5,6 , stretching or compression between two microplates [7][8][9] , optical tweezers 10,11 , and magnetic twisting cytometry 12,13 . However, indentation with the atomic force microscope (AFM) remains one of the most popular methods for probing the nanoscale properties of soft samples like cells, tissues and hydrogels [14][15][16][17] . In the AFM, the elastic properties of live cells are usually evaluated from force versus displacement (F-Z) curves. Then the Hertz model or its modifications are applied to the approach part of the F-Z curve to extract Young's modulus (E Hertz ), the elastic parameter used for characterization of the sample's mechanical properties 18,19 . However, such models assume a purely elastic nature of the sample, while in reality most biological samples are viscoelastic. Viscoelasticity is revealed in a clear hysteresis between the approach and retraction parts of curves 20 ; the indentation speed dependence of E Hertz values extracted from force curves with the Hertz model 11 ; the observations of force relaxation at constant indentation depth and the creep at constant loading force 21 . Approaches other than the standard F-Z curves are usually used to obtain the viscoelastic properties of samples with AFM in both the time [22][23][24] and frequency domains [25][26][27][28][29][30] . These generally require modifications in the AFM apparatus and/or in the data acquisition protocol. Equally importantly, each approach has its own sets of measurement uncertainties.If a standard F-Z curve could also be used to quantify viscoelastic properties, it would allow one standard method with well quantified uncertainties 31 to be used for both viscoelasticity and elasticity measurements. This has not been possible to date, we believe, due to the lack of a mathematical/computational framework that allows the post-processing of force-displacement data to extract the relevant viscoelastic constitutive parameters.