<p>Contactless, laser-based resonant ultrasound spectroscopy was utilized to monitor changes in elastic properties in single-crystalline NiTi shape memory alloy. It was observed that the elastic behavior of the temperature-induced B19′ martensite, which is formed by a fine mixture of variants, adopts the symmetry elements of the parent austenite phase and thus, the changes over the transformation temperature can be represented by the temperature evolution of three cubic elastic coefficients. The experiments confirm that the transition during the cooling run is preceded by pronounced softening of the <i>c</i>₄₄ elastic coefficient, which leads to nearly complete vanishing of elastic anisotropy prior to the transition. Below the transition, this coefficient remains soft, and the character of anisotropy switches from <i>c</i>₄₄/<i>c</i>′ &gt; 1 to <i>c</i>₄₄/<i>c</i>′ &lt; 1. We rationalize this behavior from the mechanical instability of the B19′ lattice with respect to shears along the (001)_B19′ plane, which is known from first-principles calculations.</p>