We have investigated the behavior of the depairing current J dp in ferromagnet/superconductor/ferromagnet (F/S/F) trilayers as function of the thickness d s of the superconducting layers. Theoretically, J dp depends on the superconducting order parameter or the pair-density function, which is not homogeneous across the film due to the proximity effect. We use a proximity-effect model with two parameters ͑proximity strength and interface transparency͒, which can also describe the dependence of the superconducting transition temperature T c on d s . We compare the computations with the experimentally determined zero-field critical current J c0 of small strips ͑typically 5-m wide͒ of Fe/Nb/Fe trilayers with varying thickness d Nb of the Nb layer. Near T c the temperature dependence J c0 (T) is in good agreement with the expected behavior, which allows extrapolation to Tϭ0. Both the absolute values of J c0 (0) and the dependence on d Nb agree with the expectations for the depairing current. We conclude that J dp is correctly determined, notwithstanding the fact that the strip width is larger than both the superconducting penetration depth and the superconducting coherence length, and that J dp (d s ) is correctly described by the model.