Abstract Abstract Direct numerical simulation of the non‐linear equations, governing a fluid–structure system, relies heavily on the properties of the coupled system and the corresponding iterative solver. The purpose of this paper is to introduce a flexible and robust multilevel finite element algorithm that can be used to study the behavior of a fully coupled fluid–structure system. The method relies on the domain decomposition characteristics of the multigrid Vanka solvers, which decompose the complex global domain into the finite element local sub‐domains and then compute the global solution iteratively. This particular methodology allows us to solve easily this coupled system over a fluid–solid domain which consists of a set of subdomains from different mesh levels with conforming or non‐conforming finite element method approximations. The multigrid projection and restriction operators are used to impose the matching between the extended fluid and solid velocity field. Copyright © 2007 John Wiley & Sons, Ltd.