  We evaluate the dimensionless non-Gaussianity parameter $h_{_{\rm NL}}$, that
characterizes the amplitude of the tensor bispectrum, numerically for a class
of two field inflationary models such as double inflation, hybrid inflation and
aligned natural inflation. We compare the numerical results with the slow roll
results which can be obtained analytically. In the context of double inflation,
we also investigate the effects on $h_{_{\rm NL}}$ due to curved trajectories
in the field space. We explicitly examine the validity of the consistency
relation governing the tensor bispectrum in the squeezed limit. Lastly, we
discuss the contribution to $h_{_{\rm NL}}$ due to the epoch of preheating in
two field models.
