Quasi-static compression experiments of TiZrHf-based high-entropy alloys with different trace elements (Al, Cu and Ni) are performed. The microscopic morphology and phase structure of the samples are characterised. The critical stress is determined by the fracture criterion combined. The ignition processes during the quasi-static compression process are collected, and the ignition gestation period and duration are obtained. The results show that the samples experience elastic deformation, strengthening and fracture. The failure mode is a brittle fracture. The reaction of TiZrHfCu 0.3 is more intense than TiZrHfAl 0.3 and TiZrHfNi 0.3 , and the ignition critical stress is the highest. The ignition of high-entropy alloys is induced by the joint action of crack tip discharge and chemical bond fracture in the process of crack initiation and propagation.