The first Elinvar alloy, FeNiCr, which has invariant elastic modulus over a wide temperature range, was discovered almost 100 years ago by Guillaume. The physical origin of such an anomaly has been attributed to the magnetic phase transition taking place in the system. However, the recent discovery of non-magnetic Elinvar such as multi-functional β-type Ti alloys has imposed a new challenge to the existing theories. In this study we show that random field from stress-carrying defects could suppress the sharp first-order martensitic transformation into a continuous strain glass transition, leading to continued formation and confined growth of nano-domains of martensite in a broad temperature range. Accompanying such a unique transition, there is a gradual softening of the elastic modulus over a wide temperature range, which compensates the normal modulus hardening due to anharmonic atomic vibration, resulting in a low and temperature-independent elastic modulus. The abundance of austenite/martensite interfaces are found responsible for the low elastic modulus.