  The rare decays B_s -> \mu^+\mu^- and B -> K^{(*)}\mu^+\mu^- are sensitive to
new particles and couplings via their interferences with the standard model
contributions. Recently, the upper bound on B(B_s -> \mu^+\mu^-) has been
improved significantly by the CMS, LHCb, CDF, and D{\O} experiments. Combining
with the measurements of B(B-> K^{(*)}\mu^+\mu^-), we derive constraints on the
relevant parameters of minimal supersymmetic standard model with and without
R-parity, and examine their contributions to the dimuon forward-backward
asymmetry in B-> K^{*}\mu^+\mu^- decay. We find that (i) the contribution of
R-parity violating coupling products
\lambda^{\prime}_{2i2}\lambda^{\prime*}_{2i3} due to squark exchange is
comparable with the theoretical uncertainties in B-> K \mu^+\mu^- decay, but
still could be significant in B-> K^{*}\mu^+\mu^- decay and could account for
the forward-backward asymmetry in all dimuon invariant mass regions; (ii) the
constrained mass insertion (\delta^{u}_{LL})_{23} could have significant
contribution to dA_{FB}(B-> K^{*}\mu^+\mu^-)/ds, and such effects are favored
by thr recent results of the Belle, CDF, and LHCb experiments.
