The stagnation-point of oncoming flow impinging on a stretchable flat plate or a circular cylinder is the subject of the present paper. Exact solutions are targeted for both momentum and thermal fields. Identified analytical solutions are significant as they constitute further exact solutions to the Navier & ndash; Stokes and energy equations. These solutions are deduced to be well-known particular solutions in the limiting cases of permeable stationary body surfaces. Findings reveal that stretching has suppressing effect on the axial velocity and temperature distributions. The character of flow impingement is closely adjusted by the relevant physical parameters. Heat transfer rates from the surfaces in both flow geometries are enhanced by the action of walls, with more cooled surfaces in the presence of wall suction.