The present article addresses the stagnation point flow of Jeffrey liquid towards a stretching cylinder. Heat transfer is analyzed in view of non-Fourier heat flux and thermal stratification. Expression of heat flux is based upon Cattaneo-Christov theory. Cattaneo-Christov heat flux model is utilized for the development of energy equation. Such consideration accounts the contribution by thermal relaxation. The series solutions for resulting flow and heat transfer problems have been computed. Interval of convergence for the obtained series solutions is explicitly determined. Physical quantities of interest have been examined for the influential variables entering into the problems. It is observed that velocity profile shows decreasing behavior for larger Deborah number. Further that temperature distribution decreases for larger values of thermally stratification and thermal relaxation parameters. (C) 2016 Elsevier Ltd. All rights reserved.