Several modalities of tomography have been developed for medical applications. Some example are x-ray tomography, positron emission tomography and magnetic resonance imaging which are used routinely in the clinical enviroment and electricall impedance tomography, still considered a research technique. During the seventies, measurements of the weak fields produced by the human body with unprecendet signal to noise ratio were made possible with the use of SQUIDs (Superconducting Quantum Interference Device). Magnetic susceptibility is a physical property of the matter including biological tissues to interact with an applied magnetic field. A technique to reconstruct three-dimensional susceptibity distribuition from measurements of the pertubartion of the magnetic field was studied and improved. Simulations to reconstruct the three-dimensional susceptibility distribution of a body from the measurement in the presence of noise were carried out and the tomographic reconstruction from the measurement in the presence of noise were carried out and the tomographic reconstruction from experimental measurement in the presence of noise were carried out and the tomographic reconstruction from experimental measurements with acrylic samples performed. Although this new modality of tomography presents severe spatial resolution limitation, it represents a new source of informatio from the interior of body with promising applications in the biomedical field and nondestrutive evaluations.