The choice of boundary conditions has a significant effect on the flow characteristics. In certain scenarios, such as blood flow in aortic vessels, fluid slip at boundaries must be considered, necessitating the incorporation of slipping boundary conditions. Within the context of fluid-structure interaction (FSI) problems, this calls for the development of methods that can treat slipping mechanisms at the interface between a flowing fluid and deformable walls. We present a robust and efficient numerical method for solving three-dimensional FSI problems with Navier's slip interface conditions, developed within the framework of the arbitrary Lagrangian-Eulerian (ALE) approach. The effectiveness of the approach is demonstrated through its application to blood flow simulations in aortic vessels, see Figure~\ref{fig1}. The talk is based on joint work with my PhD student Jakub Fara and R. Chabiniok, J. Hron, L. Košárková, J. Málek. This work has been supported by the project No. 23-05207S financed by the Czech Science Foundation.