The optimal stiffness for soft swimming robots depends on swimming speed, which means no single stiffness can maximise efficiency in all swimming conditions. Tunable-stiffness would produce an increased range of high-efficiency swimming speeds for robots with flexible propulsors and enable soft control surfaces for steering underwater vehicles. We propose and demonstrate a method for tunable soft robotic stiffness using inflatable rubber tubes to stiffen a silicone foil through pressure and second moment of area change. We achieved double the effective stiffness of the system for an input pressure change from 0 to 0.8 bar and 2 J energy input. We achieved a resonant amplitude gain of 5 to 7 times the input amplitude and tripled the high-gain frequency range compared to a foil with fixed stiffness. These results show that changing second moment of area is an energy effective approach to tunable-stiffness robots.