A multi-dimension, time-dependent Monte Carlo code is used to compute sample gamma-ray spectra to explore whether unambiguous constraints could be obtained from gamma-ray observations of Type Ia supernovae. Both spherical and aspherical geometries are considered and it is shown that moderate departures from sphericity can produce viewing-angle effects that are at least as significant as those caused by the variation of key parameters in one-dimensional models. Thus gamma-ray data could in principle carry some geometrical information, and caution should be applied when discussing the value of gamma-ray data based only on one-dimensional explosion models. In light of the limited sensitivity of current gamma-ray observatories, the computed theoretical spectra are studied to revisit the issue of whether useful constraints could be obtained for moderately nearby objects. The most useful gamma-ray measurements are likely to be of the light curve and time-dependent hardness ratios, but sensitivity higher than currently available, particularly at relatively hard energies (~2-3 MeV), is desirable.
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