With Kramers theory and Wentzel-Kramers-Brillouin (WKB) approximation theory, the thermal escape and macroscopic quantum tunneling behaviors of the metastable state in a three-junction flux qubit are investigated. At temperature ranging from 0.01 K to 4.2 K, the escape rate is calculated, the switching distribution which varies with magnetic field and temperature is worked out and the case of superconducting interferometer is also compared quantitatively. The results show that self-noise of three-junction flux qubit is bigger than that of superconducting interferometer.