In this paper, the enclosing control problem of second-order multi-agent systems is considered, where the targets can be either stationary or moving. The objective is to achieve an equidistant circular formation for a group of agents to enclose a team of targets. In order to do so, we first introduce a formal definition explaining certain basic properties of the exploring relation between the agents and the targets. We then construct the estimator of the centre of the targets, which is used to build the control protocol to achieve equidistant circular enclosing. Using a Lyapunov function and Lasalle's Invariance Principle, the convergency of the estimator and control protocol are, respectively, established. We then construct a smooth function to approximate the discontinuous term in the estimator. Finally, the simulations for stationary targets and moving targets are given to verify the validity of the results obtained.