AbstractIn this contribution an approach to model fluid‐structure interaction (FSI) problems with monolithic coupling is presented. The fluid as well as the structural domain are discretized using the least‐squares finite element method (LSFEM), whose application results in a minimization problem with symmetric positive definite systems also for non self‐adjoint operators, see e.g. [2]. In this study, the second‐order systems are reduced to first‐order systems by introducing new variables, which leads to least‐squares formulations for both domains based on the stresses and velocities as presented in e.g. [5] and [7]. A conforming discretization of the unknown fields in H1 and H(div) using Lagrange interpolation polynomials and vector‐valued Raviart‐Thomas interpolations functions, respectively, leads to the inherent fulfillment of the FSI coupling conditions. In more detail, a discretization in H1 ensures continuity of the velocity field and a discretization in H(div) results in continuity of the normal stress components at the interface.