A flexible fiber model based on the discrete element method (DEM) is presented and validated for the simulation of uniaxial compression of flexible fibers in a cylindrical container. It is found that the contact force models in the DEM simulations have a significant impact on compressive forces exerted on the fiber bed. Only when the geometry-dependent normal contact force model and the static friction model are employed, the simulation results are in good agreement with experimental results. Systematic simulation studies show that the compressive force initially increases and eventually saturates with an increase in the fiber-fiber friction coefficient, and the fiber-fiber contact forces follow a similar trend. The compressive force and lateral shear-to-normal stress ratio increase linearly with increasing fiber-wall friction coefficient. In uniaxial compression of frictional fibers, more static friction contacts occur than dynamic friction contacts with static friction becoming more predominant as the fiber-fiber friction coefficient increases.