Transmission　of　heat　and　mass　in　boundary　layer　flows　over　stretching　surfaces　play　a　significant　role　in　metallurgy　and　polymer　industry.　In　Current　article　the　assisting　and　opposing　flow　of　a　second　grade　fluid　towards　a　stretching　sheet　is　analyzed　to　examine　the　heat　and　mass　transfer　in　stagnation　point　boundary　layer　flow.　Different　flow　parameters　such　as　concentration,　surface　temperature　and　stretching　velocity　are　supposed　to　variate　linearly.　The　basic　transport　equations　are　transformed　into　non-linear　ordinary　differential　equations　by　means　of　boundary　layer　approximation　and　similarity　transmutations,　which　are　then　solved　by　employing　nonlinear　shooting　(NLS)　and　Keller-box　methods　(KBM).　These　techniques　are　very　useful　for　solving　boundary-layer　problems　and　are　applicable　to　other　general　situations　than　that　presented　current　study.　The　outcomes　of　velocity,　temperature,　concentration　profile,　skin-friction　coefficient,　heat　and　mass　transfer　coefficients　are　analyzed　briefly　in　graphical　and　tabular　formats.　The　mass　transmission　rate　was　found　to　be　in　direct　relation　with　Schmidt　number.　Moreover,　we　predict　that　a　rise　in　Prandtl　number　leads　to　a　decline　in　temperature　and　thermal　layer　of　boundary　thickness　for　both　supporting　and　contrasting　flows.　The　outcomes　of　this　article　are　important　for　the　analysts　in　the　field　of　second　grade　fluids.　We　believe　that　the　article　is　very　well　prepared　and　the　results　are　original　and　useful　from　both　theoretical　and　application　point　of　views.