The two-dimensional contact problem for a semi-infinite anisotropic el
astic media is reconsidered here by using the formalism of Eshelby et
al. (1953) and Stroh (1958). The approach of analytic function continu
ation is employed to investigate the half-space contact problem with v
arious mixed boundary conditions applied to the half-space. A key poin
t of the solution procedure suggested in the present paper is its depe
ndence on a general eigenvalue problem involving a Hermitian matrix. T
his eigenvalue problem is analogous to the one encountered when invest
igating the behavior of an interface crack (Ting, 1986). As an applica
tion, the interaction between a dislocation and a contact strip is sol
ved. The compactness of the results shows their potential for utilizat
ion to solve the problem of contact of a damaged anisotropic half-spac
e.