We investigate the draw resonance phenomenon in a melt spinning process by using a multi-scale simulation method (MSS) where the macroscopic model and microscopic molecular model are directly connected through the stress field. In the MSS method, we introduce Lagrangian particles which contain many molecules to precisely maintain the microscopic states. By comparing our results with the ones obtained by a conventional method using a constitutive equation in the Eulerian picture, we found the explicit relation between the macroscopic flow and microscopic states. In this research, we used the slip-link model as the microscopic polymer model, and discuss the orientation and entanglement of it.