The accurate characterization of pulmonary airways on CT is potentially very useful for diagnosis and evaluation of lung diseases. The task is challenging due to their small size and variable orientation. We propose a probabilistic modeling technique and a set of measurement tools to quantitate airway morphology. We extract the airway tree structure from high resolution CT scans with a seeded region growing algorithm. Individual airway branches are identified by reducing the airway tree to a set of central axes. Properties such as lumen diameter and branch angle are measured from these central axes. The structure of the Bayesian model is inferred from a set of equations representing the parent-daughter relationships between branches, such as equations of air flow ratio and flow conservation. The CT measurements are used to instantiate the conditional probability tables of the Bayesian model. To evaluate the model, it was used to predict the airway diameter for the 2nd, 3rd, 4th, 5th, and 6th generations of the airway tree. We show that the model can reasonably predict the diameter of a particular airway branch, given information of its parent.