Molecular model approach has been used to predict the dispersion characteristics of flexible polymer chains in confined geometries. The analysis ranges from the early stage dispersion to the steady Taylor dispersion of the simple linear dumbbell model polymer chains. For the early stage dispersion, the ray method was applied; and Aris type moments mothod was useful for the Taylor dispersion. Two parallel plates were chosen as a confining geometry and the specific initial condition of a point source in the midway of the gap was chosen for simplicity. It was found that the qualitative difference in dispersion properties of deformable polymer chains starts from the early stage compared with those of single Brownian particles. And it turns out that one parameter, which is similar to the relative spacing of the dumbbell to the gap of confining geometries, is useful to see the dispersion characteristics of the dumbbells.