The $b\to s\gamma$ decay in SUSY models with non-universal A-terms

We analyse the predictions for the inclusive branching ratio for $b\to s\gamma$ decay in a class of string-inspired SUSY models with non-universal soft-breaking A-terms. These models are particularly interesting since the non-universality of the A-terms plays an important role in providing new significant contributions to CP violation effects in kaon physics while respecting the severe bounds on electric dipole moments. We show that $b\to s\gamma$ do not severely constrain the non-universality of these models. In particular, at low $\tan\beta$ $(\tan\beta\simeq 2)$, our predictions are close to the universal case. For large $\tan\beta$ ($\tan\beta \gsim 15$),the effect of non-universality is enhanced and stronger constraints hold. We find that the parameter regions which are important for generating sizeable contribution to $\epsilon'/\epsilon$, of order $2 \times 10^{-3}$, are not excluded.