In this paper, we focus on investigating the influence on hydrodynamic factors of different coupled computational models describing the interaction between an incompressible fluid and two symmetric elastic or poroelastic structures. The fluid region is governed by time dependent Navier-Stokes equations; while for the structure region, we employ two different types of fully dynamic models to study the effects of elasticity and poroelasticity. It is known that blood flow shows a non- Newtonian property in small vessels and in situations of complex geometries. On one hand, we perform numerical experiments for blood flow using the Carreau-Yasuda model to simulate the viscosity and study the influence of non-Newtonian blood rheology as well as the poroelasticity on a benchmark vessel, by means of comparing computational results with models with Newtonian fluids or elastic structures. On the other hand, we present a two-dimensional simulation of blood flow in an axisymmetric stenosis artery, considering not only the non-Newtonian fluids properties but also the fluid-structure interaction. The results of this study demonstrate that the flow characteristics, including velocity and pressure fields, wall shear stress, relative residence time, displacement and filtration velocity, are affected by different models, geometries and parameters, such as permeability and Lam ́e coefficients.