  We consider the Lam\'{e} system arising from high-contrast composite
materials whose inclusions (fibers) are nearly touching the matrix boundary.
The stress, which is the gradient of the solution, always concentrates highly
in the narrow regions between the inclusions and the external boundary. This
paper aims to provide a complete characterization in terms of the singularities
of the stress concentration by accurately capturing all the blow-up factor
matrices and making clear the dependence on the Lam\'{e} constants and the
curvature parameters of geometry. Moreover, the precise asymptotic expansions
of the stress concentration are also presented in the presence of a strictly
convex inclusion close to touching the external boundary for the convenience of
application.
