Timely delivery of first aid supplies is significant to saving lives when an accident happens. Among the promising solutions provided for such scenarios, the application of unmanned vehicles has attracted ever more attention. However, such scenarios are often very complex, while the existing studies have not fully addressed the trajectory optimization problem of multiple unmanned ground vehicles (multi-UGVs) against the scenario. This study focuses on multi-UGVs trajectory optimization in the sight of first aid supply delivery tasks in mass accidents. A two-stage completely decoupling fuzzy multiobjective optimization strategy is designed. On the first stage, with the proposed timescale involved tridimensional tunneled collision-free trajectory (TITTCT) algorithm, collision-free coarse tunnels are build within a tridimensional coordinate system, respectively, for the UGVs as the corresponding configuration space for a further multiobjective optimization. On the second stage, a fuzzy multiobjective transcription method is designed to solve the decoupled optimal control problem (OCP) within the configuration space with the consideration of priority constrains. Following the two-stage design, the computational time is significantly reduced when achieving an optimal solution of the multi-UGV trajectory planning, which is crucial in a first aid task. In addition, other objectives are optimized with the aspiration level reflected. Simulation studies and experiments have been curried out to testify the effectiveness and the improved computational performance of the proposed design.