In this paper, a flexible piezoelectric micromachined ultrasonic transducer (PMUT) based on Scandium (Sc)-doped Aluminum Nitride (AlN) film was designed and modeled by the three-dimensional finite element method (3D-FEM). The resonant frequency of 218.1 kHz was reported. It was noticeable that a high effective electromechanical coupling coefficient (k2eff) of 1.45% was obtained when a combination of a flexible PI and a thin Si layer was used as the PMUT supporting structure layer. Compared with a pure Si supporting layer counterpart, the coupling coefficient had been improved by 110.68%. Additionally, the increase of Sc doping concentration in AlN film further enhanced the device electromechanical coupling coefficient and resulted in an improvement for transmitting/receiving sensitivity of the proposed flexible PMUT. When the doping concentration of Sc reached 30%, the emission sensitivity was as large as 1.721 μm/V, which was 2.86 times greater than that of conventional AlN film-based PMUT. The receiving sensitivity was found to be 2.11 V/KPa, which was as high as 1.23 times the performance of an undoped device. Furthermore, the bending simulation result showed that the proposed flexible PMUT device can maintain a good mechanical stability when the bending radius is greater than 1.5 mm. The simulation of sound field characteristics demonstrated that the flexible PMUT based on AlScN could receive stable sound pressure signals under the bending radius of 1.5 cm.