SUMMARYMany physical and biological systems involve inextensible fibers immersed in a fluid; examples include cilia, polymer suspensions, and actin filament transport. In such systems, the dynamics of the immersed fibers may play a significant role in the observed macroscale fluid dynamics. In this study, we simulate the dynamics of an approximately inextensible semi‐flexible fiber immersed in a two‐dimensional cellular background flow. The system is modeled as an immersed boundary problem with the fluid dynamics described using the Stokes equations. The motion of the immersed fiber is computed by means of the method of regularized Stokeslets, which allows one to calculate fluid velocity, pressure, and stress in the Stokes fluid flow regime because of a collection of regularized point forces without computing fluid velocities on an underlying grid. Simulation results show that, for some parameter values, the fiber may buckle when approaching a stagnation point. These results provide insight into the stretch–coil transition and macroscale random walk behavior that have been reported in mathematical and experimental literature. Copyright © 2011 John Wiley & Sons, Ltd.