In this paper, we study the set target aggregation problem of multiple mechanical systems. Each system is modeled by a Lagrangian dynamical equation and observes a convex set as its local target. The objective of the group is to reach an aggregation towards these target sets.We propose a set target aggregation algorithm that is constructed based on each mechanical system's own target sensing and the exchange of its information with local neighbors. With necessary connectivity for both fixed and switching communication topologies, multiple mechanical systems are shown to converge to the intersection of all the local target sets while the vectors of generalized coordinate derivatives are driven to zero. Simulations are given to validate the theoretical results.