Short linear molecules exhibit rotational motion and orientational preferences under sheared flow. This paper describes a series of molecular-dynamics simulations of fluids consisting of various kinds of short linear chain molecules that are forced to flow through a channel bounded by rough, parallel walls (Poiseuille flow). The molecules are constructed of soft spheres; these are linked in different ways to produce either fully flexible chains, stiff chains with restricted internal ce:degrees of freedom, or rigid rodlike molecules. The channel walls act as nonslip boundaries and also serve to absorb the thermal energy generated by the shear motion. For each kind of molecule, the rotational motion and orientation distributions are explored as functions of the cross-stream position. The variation in orientation shows that there is a competition between the Maxwell orientation, where the molecule is aligned at [Formula Presented] to the flow, and a tendency for molecules close to the walls to align parallel to the direction of flow. The orientational effects become more pronounced with increasing molecular stiffness.