A model is proposed which simulates brittle fracture propagation and arrest of steel with finite thickness. Based on the critical stress criterion for brittle fracture and on stress field solution for dynamically running crack in an elastic-plastic solid, dynamic fracture toughness ( K_D ) is calculated as a function of temperature and crack velocity. The calculated K_D once decreases and then increases with increasing crack velocity. Upper limit crack velocity coincides with the plastic surface wave speed and decreases with increasing temperature. The predicted dependencies of K_D on temperature and crack velocity agree with previously established experimental data. Effects of side-ligament formed near the plate surface and crack-tunneling at the inside of the plate are also taken into account for simulating the brittle crack propagation. The model predicts crack velocity, shear lip thickness, aspect ratio of the tunneling crack from the fundamental mechanical properties of steel. The model also predicts a lower bound value of applied stress intensity factor and crack velocity, the former of which may correspond to the arrest toughness, K_ca .