Abstract: A numerical study is carried out on the flow and heat transfer characteristics of a visco-elastic fluid (Walters` liquid-B model) past a stretching sheet in a porous medium considering the influence of radiation. The boundary layer equations together with the appropriate boundary conditions are first transformed by a similarity transformation into a system of ordinary differential equations. The similarity equations are then solved numerically by using the fourth order Runge-Kutta scheme with the help of shooting method. Two cases of heat transfer are considered- (1) The sheet with Prescribed Surface Temperature (PST case) and (2) The sheet with Prescribed Heat Flux (PHF case). The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The velocity and temperature profiles are graphically presented for various influencing parameters in non-dimensional form such as radiation number, Prandtl number, visco-elastic parameter, permeability parameter and heat source/sink parameter. The study has shown that the numerical technique used herein, can be advantageously used to solve the boundary value problem of a fluid flow and to assess temperature variation within the boundary.