One of the major problems in nondestructive evaluation (NDE) is the evaluation of flaw sizes and locations in a limited inspectability environment. In NDE x-ray radiography, this frequently occurs when the geometry of the part under test does not allow x-ray penetration in certain directions. Other times, the inspection setup in the field does not allow for inspection at all angles around the object. This dissertation presents a model based reconstruction technique which requires a small number of x-ray projections from one side of the object under test. The estimation and reconstruction of model parameters rather than the flaw distribution itself requires much less information, thereby reducing the number of required projections. Crack-like flaws are modeled as piecewise linear curves (connected points) and are reconstructed stereographically from at least two projections by matching corresponding endpoints of the linear segments. Volumetric flaws are modeled as ellipsoids and elliptical slices through ellipsoids. The elliptical principal axes lengths, orientation angles and locations are estimated by fitting a forward model to the projection data. The fitting procedure is highly nonlinear and requires stereographic projections to obtain initial estimates of the model parameters. The methods are tested both on simulated and experimental data. Comparisons are made with models from the field of stereology. Finally, analysis of reconstruction errors is presented for both models.