Nanotubes have been shown to possess intriguing mass transport properties, and are being incorporated into polymeric membranes for molecular separations. Although models have been developed to predict the effective permeability and selectivity of composite membranes with non-spherical fillers, they only apply to fillers with isotropic transport properties. However, molecular transport in tubular fillers is essentially one-dimensional. Here, an analytical model is developed - including the orientational distribution, aspect ratio, volume fraction, permeability of the fillers, and membrane non-idealities - to describe molecular transport in composite membranes with tubular fillers. Using the model, the effects of various structural and operational parameters of the composite membrane are assessed. It is found that the filler volume fraction, as opposed to the filler orientation, intrinsic permeability, and aspect ratio, has the most significant impact on the membrane permeability. Several case studies of binary mixture separations by ideal and non-ideal composite membranes with tubular fillers are discussed. Finally, an advanced composite membrane configuration that allows exploitation of the unique transport properties of tubular fillers is discussed. (C) 2011 Elsevier B.V. All rights reserved.