Nanomaterials are widely used in different fields, such as microelectronics, industry, and nanocomposites, and they can exhibit unstable deformation behaviour depending on the strain rates. Under strain rates of 10−4–10−1 s−1, the deformation of nanomaterials, unlike the quasi-static deformation of micromaterials, is characterized by the presence of the rate sensitivity as a possible scale phenomenon in dynamic plasticity. In this paper, the relaxation model of plasticity for the prediction of deformation curves at different strain rates is used. It allows us to comprehensively study the effects of strain hardening in a wide range of deformation conditions for coarse-grained
materials and nanomaterials. Considering the plastic deformation of the nanosized samples in the early stages, dynamical softening, associated with a generation of new defects, and dynamic hardening, are crucial. The proposed model, using one parameter or the classical hardening law as an example of nanosized gold whisker crystals, tungsten single-crystal pillars, and single-crystalline Au-Ag alloy nanowires, is verified. Calculated sets of parameters of characteristic time, as a parameter of rate sensitivity of a material, and hardening parameters for different nanomaterials are compared. It is shown that the characteristic relaxation times for the single-crystal nanomaterials (100–103 s) are greater than for the nanostructured materials (10−6–10−4 s). Despite the manifestation of dynamics at different strain rates of nanomaterials, single crystal and nanostructured materials, the proposed model can be successfully applied to materials with different degrees of hardening or softening