A two-dimensional (2D) flow of an incompressible Williamson fluid of Cattaneo-Christov heat flux type over a linearly stretched surface with the influence of magnetic field, thermal radiation-diffusion, heat generation and viscous dissipation is carried out in the present study. To develop a Williamson flow model, a boundary layer approximation is taken into account. The non-dimensional, nonlinear, coupled ordinary differential equations with boundary condition are solved numerically using Nactsheim-Swigert shooting iteration technique together with Runge-Kutta six order iteration scheme. The influences of physical parameters on the velocity, temperature, concentration is analysed through graphical consequences. To validate the accuracy of the numerical simulations scheme, comparisons is carried out with the previous studies and are found in an excellent agreement.