<p>Considering quadrotor unmanned aerial vehicles (UAVs) as actuators for the transportation of flexible loads, this paper studies dynamic modeling and quadrotor placement optimization of the UAV transportation system with rigid connections between UAVs and the flexible load. The detailed dynamics of the UAV transportation system, including the translation equation, the rotation equation and the vibration equation, are derived using the Lagrange equation of the second kind. Based on the system frequency characteristic and the control performance, two different optimization indexes are proposed. The genetic algorithm is used to determine the optimal locations of UAVs on the flexible load. Different cases with different number of UAVs for the transportation of flexible loads comprised by different materials and different number of finite element nodes are investigated. Numerical simulations are performed to illustrate the feasibility of the optimized configurations using a proportional-derivative controller. Simulation results show that the optimized configurations obtained from the system frequency characteristic index can achieve a good hovering performance of UAVs with small elastic deformations of flexible loads.</p>