In this paper, the prediction of the magnetohydrodynamic boundary layer slip flow over a permeable stretched cylinder with chemical reaction is investigated by using some mathematical techniques, namely Runge–Kutta fourth order method along with shooting technique and artificial neural network (ANN). A numerical method is implemented to approximate the flow of heat and mass transfer characteristics as a function of some input parameters, explicitly the curvature parameter, magnetic parameter, permeability parameter, velocity slip, Grashof number, solutal Grashof number, Prandtl number, temperature exponent, Schmidt number, concentration exponent and chemical reaction parameter. The non-linear partial differential equations of the governing flow are converted into a system of highly non-linear ordinary differential equations by using the suitable similarity transformations, which are then solved numerically by a Runge–Kutta fourth order along with shooting technique and then ANN is applied to them. The Back Propagation Neural Network is applied for forecasting the desired outputs. The reported numerical values and the ANN values are in good agreement than those published works on various special cases. According to the findings of this study, the ANN approach is reliable, effective and easily applicable for simulating heat and mass transfer flow over a stretched cylinder. © 2015 Karabuk University