Wireless power transfer (WPT) technology can be applied to autonomous underwater vehicles (AUVs) as a promising alternative. Conventional planar coils often fail to perfectly adapt to the cylindrical hull structure of AUVs, usually requiring additional mounting structures that increase the vehicle's size and weight. This paper analyzes flexible coupling coils for application in underwater inductive power transfer (U-IPT) system, which is compatible with the hull structure without other modifications. Under the flexible configuration, the inductance characteristics and the strength and distribution of the magnetic field of the coupling coils will change. Two configurations of flexible coupling coils suitable for U-IPT system are proposed. One is flat transmitting platform-curved receiver, another is curved transmitting platform-curved receiver. The characteristics of coil self-inductance and coupling coefficient under bending conditions are analyzed, and design, optimization, and comparison of the two coil configurations are conducted.