Commuter ridesharing is an effective way of reducing traffic congestion during peak hours, building friendship with colleagues and neighbors and saving commuting costs. However, to ride together efficiently, the riders need to find a meeting point. In this paper, the commuter ridesharing meeting points design problem is defined, from both set partitioning and centroid-based clustering perspectives, and an adapted k-medians clustering algorithm is proposed as solution. Validation of the effectiveness of the algorithm with a real-world dataset and study of the effects of different parameters including the cluster number and the vehicle capacity constraint are carried out. Simulation results show that the algorithm could save up to 67% mileage with a vehicle capacity of 10, 60% mileage with a vehicle capacity of 5 and 30% mileage with a vehicle capacity of 2. Simulation carried out on uniform platform based on real-world travel data is used as the research method, conclusion is derived according to the interpretation of simulation results. Contributions in this paper are mani-fold. Firstly, a systematic and thorough study of the commuter ridesharing meeting points design problem and the process of formulating it as an optimization problem and the prove of the equivalence between two formats, the set partitioning and the centroid-based clustering are elaborated. Then, an adapted k-medians clustering algorithm that can efficiently solve the ridesharing meeting points design problem theoretically is proposed. Finally, the utilization of a real-world travel dataset to further confirm the effectiveness and running time of the adapted k-medians clustering algorithm is introduced.