Viscosity of foods and their mechanical properties are essential for modeling the mechanical behaviour of foods during deformation and flow. The rheological models are used for engineering calculations, e.g., during design of food processing machines, pumping systems, packaging machines, etc. Although the classical linear rheology is a rate-independent theory, the mechanical properties of the viscoelastic plant materials depend on a deformation rate. The influence of a deformation rate on mechanical properties of biological viscoelastic materials needs to be documented and it is the aim of this paper. It is proved, based on the Maxwell model, that the modulus of elasticity and the viscosity ratio are decreasing functions of the rate of deformation. Next, the modulus of elasticity and the viscosity ratio of the carrot cylindrical samples are determined using discrete-time measurements of the reaction force obtained in the compression and relaxation tests at a wide range of preliminary deformation rates, i.e. from 1.67×10^–4 m•s^-1 to 1.5 m•s^-1. The relaxation data were processed using a four-element Maxwell model and the changes in viscoelastic constants were determined as a function of the deformation rate. The stress relaxation both in the state of uniaxial stress as well as in the state of uniaxial strain is considered. The experimental results are in good agreement with theoretical analysis for the biological material considered. The results motivate hypothesis that the number of microcrackings increases along with the deformation rate and indicate the irreversible character of the changes that proceed in plant materials under loading.