Humidification of the reactant gas streams is a key requirement for the efficient operation and durability of PEM (Proton Exchange Membrane) fuel cell systems. Flat membrane humidifiers are widely used for this purpose, transferring water vapor from the humid exhaust stream to the dry inlet gas stream(s) via thin, water-permeable planar membranes, each sandwiched between a dry and a humid flow-channel or flow-channel plates often operating in a counter-flow mode and containing turbulator elements for enhancing water transfer and providing membrane support. The performance of these humidifiers is governed by a close coupling between flow channel aerodynamics, membrane deformation, and transmembrane water transport. This work presents a coupled numerical framework for the detailed analysis of a periodic flat membrane humidifier segment as basis for the global optimization of an entire humidifier. The flowfield in the dry and humid counter-flow gas channels is computed using a FVM CFD (Finite-Volume-Method Computational Fluid Dynamics) solver. The resulting flow-induced pressures and viscous stresses acting on both sides of the membrane are then transferred as load conditions to a FEM (Finite Element Method) solver, which calculates the deformation of the membrane. The updated membrane position is subsequently communicated back to the CFD solver, directly modifying the channel geometry and, in turn, the flowfield, thereby establishing a bi-directionally coupled FSI (Fluid Structure Interaction) framework. The CFD solution also provides local water humidity on both sides of the membrane allowing to determine the water flux across the membrane in each iteration step using a separate water transfer model. Since the considered membrane consists of a functional layer and a porous support structure, it exhibits nonlinear anisotropic mechanical behavior requiring the use of adequate constitutive material models, aside from the material property data needed for calculating the water transfer.