In the context of the sixth-generation wireless communication system, the integration of UAVs for covert communication support offers significant potential for enhancing system performance due to their adaptable deployment capabilities. However, most existing studies have concentrated on the impact of a single ground obstacle on air-to-ground (A2G) communication channels and the optimal placement of UAVs. As a result, these approaches have not delivered optimal communication quality for covert transmissions. To solve this problem, we adopted a multiple-obstacle assisted multiple-UAV covert communication joint optimization method (MOA-UCCJOM), which optimizes the position and transmit power of UAVs on the basis of considering the role of multiple obstacles, so as to maximize the communication quality between the UAV (Alice) and the legal ground receiver (Bob). Specifically, we consider the irregular distribution of multiple obstacles around the ground administrator (Willie), and divide the allocation plan of the UAV into the two practical scenarios according to the conventional operating environment. In each of the 2D vertical planes specified by Willie, we narrowed down the feasible flight area for the optimal layout of the drone and, in a specific case, solved the joint optimization problem. The simulation results confirm the geometric inference, demonstrate the superiority of MOA-MUCCJOM, and prove that the UAV can achieve near-optimal performance at a specific position.