In developing neurons, molecular motors organize microtubule (MT) filaments into a parallel array that functions as a railway for intracellular vesicle transport. An essential feature of the axonal MT array is a nearly uniform polarity pattern in which MTs are oriented with their rapidly growing "plus ends" away from the cell body. Corruption of this polarity pattern in response to disease or injury is associated with disordered vesicle transport, loss of axon/dendrite differentiation, and neurodegeneration. In this talk, I will describe computational models that we developed to investigate how the uniform MT polarity pattern is established and maintained in axons. We use stochastic simulations to model the dynamic organization of the MT array in response to forces imparted to MTs by populations of molecular motors and static cross-linking proteins. In collaboration with Prof. Peter Baas at Drexel University, we are testing model predictions using live-cell imaging of MTs moving through photo-bleached axon segments.