In this paper we study the inverse problem of determining the residual stress
in Man's model using tomographic data. Theoretically, the tomographic data is
obtained at zero approximation of geometrical optics for Man's residual stress
model. For compressional waves, the inverse problem is equivalent to the
problem of inverting the longitudinal ray transform of a symmetric tensor
field. For shear waves, the inverse problem, after the linearization, leads to
another integral geometry operator which is called the mixed ray transform.
Under some restrictions on coefficients, we are able to prove the uniqueness
results in these two cases
