The shape of a polymer plays an important role in determining its interactions with other molecules and with the environment, and is in turn affected by both of them. As a consequence, in the literature the shape properties of a chain in many different conditions have been investigated. Here, we characterize the shape and orientational properties of a polymer chain under tension, a physical condition typically realized both in single-molecule experiments and in vivo. By means of analytical calculations and Monte Carlo simulations, we develop a theoretical framework which quantitatively describes these properties, highlighting the interplay between external force and chain size in determining the spatial distribution of a stretched chain.