Based on the constitutive law for mixed linear hardening materials suggested by Yu. Kadaschevich and V. V. Novozhilov, asymptotic solutions are obtained for Mode I crack during dynamic growth for plane strain and plane stress. Effects of the speed of crack propagation and the mixed hardening parameter beta on near-tip fields are investigated. The results show that the effects of crack propagating speed on the crack opening displacement rate is significant when hardening is rather weak. In addition, the effects of crack propagating speed on all the quantities are increased with the decrease of the mixed hardening parameter beta . The result is important for the development of fracture criteria.