When an inflated soft tube such as a cylindrical balloon is twisted, mechanical instability can arise and produces a kink-like radius collapsing in the middle of the tube. Here this phenomenon inspires us to theoretically analyze a standard non-linear model of rubber elasticity for soft tubes. We show that there exists a critical pressure beyond which such instability arises. The critical pressure depends on the elastic properties of the tube material and the geometric dimensions of the thin-walled tube. This general theory covers a large class of soft materials and explains why twist-induced collapsing is observable in soft and thin elastic tubes such as balloons, but not in hard and thick tubes such as water hoses.