The flow field of viscoelastic fluids is commonly analyzed by using constitutive equations. In this paper, a bead-spring-damper macro model with interaction is proposed as an alternative to analyze a viscoelastic flow. A tetrahedral structure of beads and springs models a gathering of intertwined polymer chains. Behavior of the macro model and the cluster is computed under a simple shear flow condition. Shear-thinning of viscosity, the mechanism of generation of normal stress differences and the effect of slip in the interaction are investigated. The results show that the elongation of clusters to the x direction is the mechanism of the normal stress differences generation, and that the slip in the interaction weakens the stresses. Consequently, it is found that the bead-spring-damper macro model can express the behavior of polymer chains in viscoelastic fluids and basic characteristics of viscoelastic fluids without using constitutive equations.