  We study possible effects of supersymmetry (SUSY) in CP asymmetries in
non-leptonic $B_{d,s}$ decays in a variety of SUSY flavour models considered in
literature. We use both mass insertion and vertex mixing methods to calculate
squark-gluino box diagrams contribution to $B_{d,s} - \bar{B}_{d,s}$ mixings.
With the squark mixing parameter $\eta=0.22$, and with large new CP phases, it
turns out that the CP asymmetries to be measured in upcoming B-factories,
HERA-B and LHC-B, can be completely dominated by the SUSY contribution in
almost every considered model. Discrimination between the different models can
be done by comparing experimental results in different decay modes. In some
models squark masses up to $\sim 5$ TeV can be probed through these experiments
provided the SUSY contribution to $B - \bar{B}$ mixing is at 10% level,
$|M^{SUSY}_{12}/M_{12}^{SM}|\sim 0.1.$ This implies that models with heavy
squarks have a fair chance to be tested in the future CP experiments before
LHC.
