Based on the principle of minimal energy and Stoner-Wohlfarth model, the effect of the tensile stress on the exchange bias for ferromagnetic/antiferromagnetic bilayers has been investigated. When the applied field is absent, according to the relation between the energy of the system and the orientation of ferromagnetic magnetization, the location of the intrinsic easy axes and intrinsic hard axes of the system have been obtained. It is found that the system will be in monostable state or bistable state, which is controlled by the competition between the uniaxial anisotropy and the exchange anisotropy of the system. Monostable state and bistable state of the system determine the angular dependence of exchange bias immediately. When the applied field is parallel to the intrinsic easy axes and intrinsic hard axes, by analyzing the magnetization process, we find that one of the switching field of the hysteresis loop shows a jump, while the other is kept constant, and consequently the exchange bias field and the coercivity will appear a step. Both the exchange bias field and the coercivity have a greater value at the point of step. The numerical calculations indicate that both the magnitude and the orientation of the tensile stress will significantly affect the exchange bias by making a transition between monostable state and bistable state in the system. This transition induces a significant change in angular dependence of the exchange bias. Our results demonstrate that tensile stress is a viable way to control and tune the exchange bias of the ferromagnetic/antiferromagnetic bilayers.