Summary: The laminar boundary layer flow over a non-linearly stretching two-dimensional sheet, or axisymmetric plane or the body of revolution arising from non-linear power law stretching velocity has been presented. The analysis leads to non-linear self-similar equations of N. Afzal and I. S. Varshney [The cooling of a low heat resistance stretching sheet moving through a fluid, Heat Mass Transfer 14, 289–293 (1980)], irrespective of the fact whether the stretching generates two-dimensional or axisymmetric flow. In fact, the surface stretching parameter \(\beta \) contains the property of two-dimensional or axisymmetric geometry of the flow. The non-similar solutions represented by a power series are considered, where and the higher order terms lead to linear set of ordinary differential equations. The linearity of these equations have been exploited by splitting them into universal functions which can tabulated once and for all, and numerical solution of these universal functions have been tabulated (but not presented in this paper). The solution to the universal functions have been applied for the two-dimensional stretching sheet velocity \(U_w (x) = U_{wo} (1+a_w x)\) for \(a_w>0\) and \(a_w<0\) have been encouraging. For self-similar equations, a series solution for a non-linear stretching of sheet with suction and blowing over a permeable surface have been also presented here. The thermal boundary layer closed form solution, series solution and the asymptotic solutions for very large and very small values of Prandtl numbers are also presented.