An exact similarity solution of the Navier-Stokes equations is obtained. The solution represents steady axisymmetric stagnation-point flow towards a stretching surface. It is shown that the, flow displays a boundary-layer structure when the stretching velocity of the surface is less than the free stream velocity. On the other hand, an inverted boundary layer is formed when the surface stretching velocity exceeds the free stream velocity. Temperature distribution in the flow is found when the surface is held at a constant temperature. It turns out that when the surface temperature exceeds the ambient temperature, heat flows from the surface to the fluid near the stagnation point but further away from the stagnation point, heat flows from the fluid to the stretching surface.