Liquid droplets bridging filaments are ubiquitous in nature and technology. Although the liquid-surface shape and the capillary force and torque have been studied extensively, the effect of filament flexibility is poorly understood. Here, we show that elastic deformation (at large values of the elasto-capillary number) can significantly affect the liquid-surface shape and capillary force. The equilibrium state of parallel filaments is calculated using analytical approximations and numerical solutions for the fluid interface. The results compare well, and the numerical solution is then applied to crossing filaments. In the investigated range of parameters, the capillary force increases rapidly when the filaments touch. The force decreases continuously when decreasing the liquid volume for parallel hydrophilic filaments but produces a maximum for crossed filaments. The liquid volume at the maximum force is reported when changing the filament flexibility, crossing angle, and contact angle. These results may be beneficial in applications where the strength and structure of wet fibrous materials are important, such as in paper formation and when welding flexible components.