In this paper, an analysis is carried out for the similarity solution of the steady boundary layer flow and heat transfer of a Casson nanofluid flowing over a vertical cylinder which is stretching exponentially along its radial direction. Using boundary layer approach and suitable similarity transformation the governing partial differential equations with the boundary conditions are reduced to a system of nonlinear ordinary differential equations. The resulting system is solved with the help of numerical technique, the Runge-Kutta Fehlberg method. The effects of important parameters such as Reynolds number, Prandtl number, Lewis number and the natural convection parameter are described through graphs.