To investigate the aeroelasticity effect and propulsion performance of flexible propellers, the mature computational fluid dynamics (CFD) and computational solid dynamics (CSD) softwares are used as the platform to establish an aeroelasticity analysis framework. The radial point interpolation method (RPIM) is applied to achieve the transmission of displacement, while the transfer of aerodynamic loads is assisted by the principle of virtual displacement. This method can avoid generating singular interpolation matrix. Moreover, it has numerical stability, which is suitable for nodes with arbitrary distribution. Furthermore, it can avoid energy loss during data transmission. The update of fluid domain grid is implemented by using the Delaunay mapping method. The results show that the maximum deformation of blade along the incoming flow direction can reach 9.4% of blade radius, and the deformation in the rotation plane is about 52.1% of flow direction. The deformation exerts a greater positive pressure on the windward side of the propeller, which, in turn, results in a higher thrust and torque in flexible propellers than in rigidity propellers. Their maximum changes can reach 7.2% and 9.9%, respectively. The aeroelasticity effect does not substantially affect the propulsion efficiency. Hence, the aeroelasticity effect has a greater impact on the propulsion performance when the propeller is under high thrust and low speed conditions. It can increase the thrust while basically maintaining the original efficiency.