In this work, the authors study the resource allocation problems of second‐order multi‐agent systems, where each agent is associated with a local cost function and the decisions of agents are constrained by network resource constraints. To seek the optimal resource allocation with low communication costs, a distributed algorithm with event‐triggered schemes is proposed. With the help of Lyapunov stability theory and convex analysis, the authors analyse the convergence of the algorithm and prove the event‐triggered schemes are free of Zeno behaviour. Under the proposed algorithm, the second‐order agents exponentially converge to the exact optimal decision of the resource allocation problem, and the burden of communication is reduced effectively. Finally, a simulation of the economic dispatch problem is given to illustrate the effectiveness of the authors' results.