The objective of this work was to employ artificial neural networks (NN) to solve inverse problems in different engineering fields, overcoming various obstacles in applying NN to different problems and benefiting from the experience of solving different types of inverse problems. The inverse problems investigated are: 1) damage detection in structures, 2) detection of an anomaly in a light-diffusive medium, such as human tissue using optical imaging, 3) structural optimization of fiber optic sensor design. All of these problems require solving highly complex inverse problems and the treatments benefit from employing neural networks which have strength in generalization, pattern recognition, and fault tolerance. Moreover, the neural networks for the three problems are similar, and a method found suitable for solving one type of problem can be applied for solving other types of problems. Solution of inverse problems using neural networks consists of two parts. The first is repeatedly solving the direct problem, obtaining the response of a system for known parameters and constructing the set of the solutions to be used as training sets for NN. The next step is training neural networks so that the trained neural networks can produce a set of parameters of interest for the response of the system. Mainly feed-forward backpropagation NN were used in this work. One of the obstacles in applying artificial neural networks is the need for solving the direct problem repeatedly and generating a large enough number of training sets. To reduce the time required in solving the direct problems of structural dynamics and photon transport in opaque tissue, the finite element method was used. To solve transient problems, which include some of the problems addressed here, and are computationally intensive, the modal superposition and the modal acceleration methods were employed. The need for generating a large enough number of training sets required by NN was fulfilled by automatically generating the training sets using a script program in the MATLAB environment. This program automatically generated finite element models with different parameters, and the program also included scripts that combined the whole solution processes in different engineering packages for the direct problem and the inverse problem using neural networks. Another obstacle in applying artificial neural networks in solving inverse problems is that the dimension and the size of the training sets required for the NN can be too large to use NN effectively with the available computational resources. To overcome this obstacle, Principal Component Analysis is used to reduce the dimension of the inputs for the NN without excessively impairing the integrity of the data. Orthogonal Arrays were also used to select a smaller number of training sets that can efficiently represent the given system. / Ph. D.