Modeling an aortic dissection represents a particular challenge from a numerical perspective, especially when it comes to the interaction between solid (aortic wall) and liquid (blood flow). The complexity of patient‐specific simulations requires a variety of parameters, modeling assumptions and simplifications that currently hinder their routine use in clinical settings. We present a numerical framework that captures, among other things, the layer‐specific anisotropic properties of the aortic wall, the non‐Newtonian behavior of blood, patient‐specific geometry, and patient‐specific flow conditions. We compare hemodynamic indicators and stress measurements in simulations with increasingly complex material models for the vessel tissue ranging from rigid walls to anisotropic hyperelastic materials. We find that for the present geometry and boundary conditions, rigid wall simulations produce different results than fluid–structure interaction simulations. Considering anisotropic fiber contributions in the tissue model, stress measurements in the aortic wall differ, but shear stress‐based biomarkers are less affected. In summary, the increasing complexity of the tissue model enables capturing more details. However, an extensive parameter set is also required. Since the simulation results depend on these modeling choices, variations can lead to different recommendations in clinical applications.