By modelling of inelastic wedge-shaped crystal twins in Be of the auxetic and non-auxetic states on the mesoscopic level, it is shown that the change in the Poisson coefficients’ magnitudes and signs with a temperature increasing leads to inversion of the localized stress fields near the tip and edges of the twin and to significant (by several times) decrease in the magnitude of stresses around it, near dislocations and their complexes. This effect is accompanied initially by softening of elastic modules and followed by inhibition of processes of plastic deformation and strengthening of Be during the transition to a complete auxetic state above 575 K.