Water confined to a repulsive ellipsoidal cavity with a variable aspect ratio is studied by computer simulation. The orientational order parameter of the O-H bond with respect to the symmetry axis of the cavity, S O H , is examined as a function of the cavity dimensions for finite numbers of water molecules (N = 6 to 38 at constant density). We observe that the absolute value of S O H is increased by deforming a spherical cavity into either a prolate or an oblate ellipsoidal cavity. This trend is method independent, i.e., it is obtained using Monte Carlo simulations with TIP4P or SPC water and using molecular dynamics simulations. Generally S O H decreases with increasing N and temperature for a fixed cavity aspect ratio. The calculated magnitudes of S O H and its temperature dependence are in order-of-magnitude agreement with experimental NMR determinations of S O H in hydrated fibers. Hence such spatial anisotropies should be considered in models of the residual orientation exhibited by probe molecules in fibrous synthetic and biological materials.