This paper introduces a new approach to the problem of quantitatively reconstructing cylindrically symmetric ob jects from radiograph data obtained via x-ray tomography. Specif- ically, a mixed variable programming (MVP) problem is formulated, in which the variables of interest are the number and types of materials and the thickness of each concentric layer. The ob jective function is a measure of distance between one-dimensional radiograph data and a material property vector operated on by a forward pro jection based on the Abel trans- form. The mixed variable pattern search (MVPS) algorithm for linearly constrained MVP problems is applied to the problem by means of the NOMADm MATLAB