In this paper, we study the influence of the scaling functions in Perzyna\u27s type elasto-viscoplastic models for predicting time-dependent behaviour of natural clays. The constitutive models were developed based on the overstress theory with different scaling functions and on the elastoplastic model S-CLAY1S which accounts for induced anisotropy and gradual degradation of apparent soil bonds. Laboratory tests were simulated on natural clays under one-dimensional and triaxial conditions to evaluate the scaling function influence in the modelling of the strain-rate effect on soil strength and creep effect. The influence of scaling functions on modelling the time-dependent behaviour under pressuremeter condition was also numerically examined. This test is treated as an example of a boundary value problem, which also allows us to see if this in situ testing is capable of deriving the parameters controlling the time-dependent behaviour