In this paper, we present an analytical solution for an infinite strip having an eccentric circular hole when the strip is subjected to in-plane bending at infinity. The analysis is based on the Papkovich-Neuber displacement potentials and the solution is obtained by a proper combination of harmonic function in integral forms and infinite series. The boundary conditions on both sides of the strip and around the hole are satisfied using the relations between the Cartesian and polar harmonics. The numerical results obtained are compared with those of FEM. A detailed stresses around the eccentric hole are illustrated for the various size of the eccentricity and the hole radius.