<p>Long-term carpooling is a convenient and stable way for demanders who travel to their destinations for a long time and have similar travel time. How to match drivers and riders effectively is a very important problem in long-term carpooling. This paper proposes a stable matching method for long-term carpooling. Firstly, the stable matching problem of long-term carpooling is described, and the relevant definitions of stable matching are given. Secondly, a mixed-integer programming model is constructed with the objective of maximizing the total utility. Then, a heuristic algorithm based on knowledge rules and Benders decomposition is proposed. Finally, numerical experiments on different scales validate the feasibility and effectiveness of the proposed method. The results show that the price of stability is relatively small compared with system optimum. On this basis, we explore how certain parameters such as the stability constraints, objective function, cost-sharing method, vehicle capacity and maximum detour ratio, might affect the matching scheme.</p>