Charitable resources, as a special type of public good, need effective management to harness public charitable energy, ensure the smooth flow of resources, and promote efficient use of charitable assets. This paper uses systematic management theory and evolutionary game theory to analyze how to manage the flow of charitable resources. The study focuses on the behaviors and cost-benefit dynamics of different groups involved in the charitable resource flow, aiming to find the best management methods to support public welfare charities and maximize benefits. The research assumes three key groups in the charitable resource system: managers, users, and suppliers. It then examines the basic elements of their interactions. By exploring how these groups optimize their strategies and affect each other’s decisions and benefits, the study establishes replicator dynamic equations. Through theoretical analysis using Lyapunov stability theory, it identifies the system’s evolutionary stable strategies, assessing if a stable equilibrium can be achieved among charitable organizations. The numerical simulations verify the theoretical findings and demonstrate the impact of different management methods on the strategies of the three stakeholders. The results provide valuable insights for managers to optimize the flow and management of charitable resources.