A catastrophe model of support and surrounding rock interaction is established. Catastrophe instability of surrounding rock is studied by using support stiffness and softening stiffness modulus of surrounding rock. The model gives rational theoretical basis of new Austrian tunnelling method. The key point of catastrophe instability is quantified. Support and surrounding rock become discrete material when its displacement get the key point. The key point is determined by internal cause rather than external cause of support and surrounding rock.