While tomographic reconstruction techniques are commonly utilized for the analysis of electromagnetic (typically x-ray) wave propagation data, this approach is infrequently used to examine acoustic data outside the geophysics community. However, acoustic tomography offers some distinct cost and performance advantages over conventional imaging techniques and some unique capabilities which are currently under investigation. One of the most intriguing of the enhanced capabilities is multiparameter imaging. In conventional ultrasonic testing, one usually concentrates on a single parameter of interest, whether it be amplitude, velocity, etc. and for most applications this is fully adequate. This is also true for most tomographic imaging situations such as x-ray tomography where attenuation is sought as the parameter to be obtained from the reconstruction process. However, in many cases, one parameter alone fails to yield full information about the material state even for isotropic media where two independent material stiffness parameters are required for complete characterization. For anisotropic media, the situation becomes increasingly complex with the degree of anisotropy with 21 independent material parameters required. In this work, we address the problem of multiparameter reconstruction and detail a way in which a standard reconstruction technique namely the algebraic reconstruction technique or ART can be modified to achieve this goal. Both isotropic and anisotropic situations are considered. Also, as a practical application of this approach, we address the problem of residual stress determination. Certainly, the use of tomography for residual stress analysis is not new. However, in all these studies, only a single residual stress parameter was reconstructed. This approach is quite satisfactory providing the stress state is uniaxial. Here, we develop a general approach for the tomographic reconstruction of a triaxial stress field.