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We report a ductile -type titanium alloy with body-centered cubic (bcc) crystal structure having a low Poisson’s ratio of 0.14. The almost identical ultralow bulk and shear moduli of combined with an ultrahigh strength of contribute to easy crystal distortion due to much-weakened chemical bonding of atoms in the crystal, leading to significant elastic softening in tension and elastic hardening in compression. The peculiar elastic and plastic deformation behaviors of the alloy are interpreted as a result of approaching the elastic limit of the bcc crystal under applied stress.