The solution of inverse problems is of interest in a variety of applications ranging from geophysical exploration to medical diagnosis and non-destructive evaluation (NDE). Electromagnetic methods are often used in the nondestructive inspection of conducting and ferromagnetic materials. A crucial problem in electromagnetic NDE is signal inversion wherein the defect parameters must be recovered from the measured signals. Iterative algorithms are commonly used to solve this inverse problem. Typical iterative inversion approaches use a numerical forward model to predict the measurement signal for a given defect profile. The desired defect profile can then be found by iteratively minimizing a cost function. The use of numerical models is computationally expensive, and therefore, alternative forward models need to be explored. This thesis proposes neural network based forward models in iterative inversion algorithms for solving inverse problems in NDE.;This study proposes two different neural network based iterative inverse problem solutions. In addition, specialized neural networks forward models that closely model the physical processes in electromagnetic NDE are proposed and used in place of numerical forward models. The first approach uses basis function networks (radial basis function (RBFNN) and wavelet basis function (WBFNN)) to approximate the mapping from the defect space to the signal space. The trained networks are then used in an iterative algorithm to estimate the profile given the measurement signal. The second approach proposes the use of two networks in a feedback configuration. This approach stabilizes the solution process and provides a confidence measure of the inversion result. Furthermore, specialized finite element model based neural networks (FENN) are proposed to model the forward problem. These networks are derived from conventional finite element models and offer several advantages over conventional numerical models as well as neural network based forward models. These neural networks are then applied in an iterative algorithm to solve the inverse problem. Results of applying these algorithms to several examples including synthetic magnetic flux leakage (MFL) data are presented.