The fluid flow due to a stretching cylinder encounters in several industrial manufacturing processes. Such processes are fiber technology, drawing of plastic films, paper production, extrusion processes and of theoretical interest etc. Present study deals with the numerical solutions for mass transfer flow problems of Newtonian and Non-Newtonian fluids. The effect of mass transfer on axisymmetric laminar boundary layer flow along a continuously stretching cylinder immersed in a viscous and incompressible fluid is investigated. The boundary layer equations in cylindrical form are first transformed into a set of non-dimensional ordinary differential equations using dimensionless variables and then solved by Runge-Kutta method with Shooting Technique. The problem under consideration reduces to the flat plate case so that the curvature parameter is absent, and thus the results obtained can be examined.