In this paper, the so‐called small time‐step instability in finite element simulation of the fluid part is considered in fluid–structure interaction (FSI) problems in which a high‐frequency vibrating structure interacts with an incompressible fluid. Such a situation is common in many microfluid manipulating devices. A treatment has been proposed that uses the dimensionless set of FSI governing equations in order to scale up the problem time step to a proper level that precludes the potential small time‐step instability. Two‐dimensional and three‐dimensional finite element simulations of a mechanical micropumping device are performed to verify the efficiency of the presented approach. Solid structure vibrations of high frequency and nano‐scale amplitude are used to derive the fluid flow in this kind of micropump. Results of FEM simulations are in good agreement with experimental data. The fluid problem is formulated and solved in arbitrary Lagrangian–Eulerian description. Copyright © 2011 John Wiley & Sons, Ltd.