  When two inclusions with high contrast material properties are located close
to each other in a homogeneous medium, stress may become arbitrarily large in
the narrow region between them. In this paper, we investigate such stress
concentration in the two-dimensional Stokes flow when inclusions are the
two-dimensional cross sections of circular cylinders of the same radii and the
background velocity field is linear. We construct two vector-valued functions
which completely capture the singular behavior of the stress and derive an
asymptotic representation formula for the stress in terms of these functions as
the distance between the two cylinders tends to zero. We then show, using the
representation formula, that the stress always blows up by proving that either
the pressure or the shear stress component of the stress tensor blows up. The
blow-up rate is shown to be $\delta^{-1/2}$, where $\delta$ is the distance
between the two cylinders. To our best knowledge, this work is the first to
rigorously derive the asymptotic solution in the narrow region for the Stokes
flow.
