The development of vehicle-to-vehicle (V2V) communication facil-itates the study of cooperative positioning (CP) techniques for vehicular applications. The CP methods can improve the posi-tioning availability and accuracy by inter-vehicle ranging and data exchange between vehicles. However, the inter-vehicle rang-ing can be easily interrupted due to many factors such as obsta-cles in-between two cars. Without inter-vehicle ranging, the other cooperative data such as vehicle positions will be wasted, leading to performance degradation of range-based CP methods. To fully utilize the cooperative data and mitigate the impact of inter-vehicle ranging loss, a novel cooperative positioning method aided by plane constraints is proposed in this paper. The positioning results received from cooperative vehicles are used to construct the road plane for each vehicle. The plane parameters are then introduced into CP scheme to impose constraints on positioning solutions. The state-of-art factor graph optimization (FGO) algo-rithm is employed to integrate the plane constraints with raw data of Global Navigation Satellite Systems (GNSS) as well as inter-vehicle ranging measurements. The proposed CP method has the ability to resist the interruptions of inter-vehicle ranging since the plane constraints are computed by just using position-related data. A vehicle can still benefit from the position data of cooperative vehicles even if the inter-vehicle ranging is unavaila-ble. The experimental results indicate the superiority of the pro-posed CP method in positioning performance over the existing methods, especially when the inter-ranging interruptions occur.