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This article presents the results of modeling the mechanical behavior of Zr–Nb and Ti–Nb alloys in a range of strain rates from 0.001 to 1000 1/s and temperature range 297–1273 K. A modification of constitutive equations describing the mechanical response of fine-grained and coarse-grained Zr–1Nb and Ti–13Nb–13Zr alloys in a wide temperature range is proposed. It was shown that the phase transition between the hexagonal closed packed and body-centered cubic crystal structure at elevated temperatures leads to a sharp change in strain rate sensitivity of the yield strength of Zr–Nb and Ti–Nb alloys. The proposed modifications of constitutive equations make it possible to describe the strain hardening and the strain rate sensitivity of the plastic flow stress over a wide temperature range in the coarse-crystalline and ultrafine-grained Zr–Nb and Ti–Nb alloys. The results can be used for engineering analysis of structural elements of technical systems and design of manufacturing technologies for biomedical products.