  In this paper we study the local behavior of a solution to the Stokes system
with singular coefficients. One of the main results is the bound on the
vanishing order of a nontrivial solution to the Stokes system, which is a
quantitative version of the strong unique continuation property. Our proof
relies on some delicate Carleman-type estimates. We first use these estimates
to derive crucial \emph{optimal} three-ball inequalities. Taking advantage of
the optimality, we then derive an upper bound on the vanishing order of any
nontrivial solution to the Stokes system from those three-ball inequalities.
