Tumors are not always lethal, but many cancers cause death when cancer cells invade important organs such as the liver, brain or lung thereby destroying the normal function of these organs. The motivation for ultrasound tomography is the location and identification of malignant human breast tissues for the purpose of detecting breast cancer. Although mammography is widely used for breast cancer detection, it has a high false positive rate and does not always accurately separate the malignant tissue from the benign tissue. Ultrasound tomography is used to compensate for these shortcomings. The malignant tissues can be separated from the benign tissues using the fact that malignant tissues have different wave speeds, attenuation, and scattering. We develop computational models for solving an inverse scattering problem arising in ultrasound imaging. To solve the inverse scattering problem, the approximate total field and unknown scattering function is found using an iterative method. The principal computational problem involved is the solution of an ill-conditioned linear system arising from an ill-posed problem written as an integral equation.