Recent advances in coil design and fabrication have allowed for flexible and thermoformed coil arrays. However, the weak solder joints and rigid design of traditional variable capacitors used with these coils greatly limit their flexibility. Here, we propose the Flexible Tunable Capacitor (FTC), a high-Q, flexible, easily tunable variable capacitor. This design uses an array of small low-loss parallel plate capacitors adjustable with small step sizes by exploiting series and parallel combinations. This work proposes a basic design that offers a wide range of capacitor values (0.5 pF to 7 pF) suitable for 3T and 7T coils.