This paper presents an approach to the reconstruction and parameter estimation of flaw models in NDE radiography. The reconstruction of flaw models rather than the flaw distribution itself reduces the required number of projections as well as the complexity of the measurement system [1,2]. In this approach, crack-like flaws are modeled as piecewise linear curves, and volumetric flaws are modeled as ellipsoids. Our emphasis here is on a method for estimating the model parameters for crack-like flaws using a linear model with more than the minimal number of required projections. Extra projections reduce the effects of measurement errors and film noise. We also present the development of the volumetric flaw model and outline a method for its inversion.