In recent years, the problem of multi-agent encirclement has attained much attention and was extensively studied. However, few work consider the factor that the on-board calculation as well as the communication capacity in the multi-agent system is limited. We investigate the encirclement control by employing the newly developed bearing rigidity theory and event-triggered mechanism. Firstly, in order to reduce the onboard loads,the event-triggered mechanism is considered in the framework and further an event-triggered control law based on bearing rigidity is proposed. The input-to-state stability(ISS) of networked agents is also analyzed by using the Lyapunov method and the cyclic-small-gain theory. In addition, the lower bound for the inter-event times is provided. Finally, to verify the efficiency and feasibility of the proposed encirclement control law, numerical experiments are investigated. In recent years, the problem of multi-agent encirclement has attained much attention and was extensively studied. However, few work consider the factor that the on-board calculation as well as the as communication capacity in the multi-agent system is limited. the encirclement control by employing the new developed bearing rigidity theory and event-triggered mechanism. First, in order to reduce the onboard loads, the event-triggered mechanism is considered in the framework and further an event-triggered control law based on bearing rigidity is proposed. The input-to-state stability (ISS) of networked agents is also analyzed by using the Lyapunov method and the cyclic-small-gain theory. Finally, to verify the efficiency and feasibility of the proposed elevatory encirclement control law, numerical experiments are investigated.