In this research paper, a numerical investigation of effects of Reynolds number and Elastic number, using MATLAB built in bvp4c solver technique has been done on Walter B fluid flow past a vertical channel. The suitable similarity transformation has been adopted to convert the boundary layer governing equations (Partial Differential Equations) into its corresponding solvable ordinary differential equations and these equations are solved using MATLAB bvp4c scheme. The normal and tangential velocity profiles are drawn for various values of parameter such as Reynolds number (Re) and Elastic number (S) and results are analysed graphically. It is perceived that with enhance of Reynolds number as well as Elastic number the normal velocity profile enhances. Further an error analysis has been done by comparing the work with the results obtained from Homotopy Perturbation Method and the comparison is found to be in very good agreement.