Consider steady flow generated by a uniform velocity field past a fixed closed slender body whose major axis is aligned closely to the uniform stream direction. Let us assume Oseen flow with the slip boundary condition. A slender–body theory is presented. In the near field, let us assume that the second–derivative changes in the velocity and pressure fields are of lower order in the axial direction of the slender body than in the transverse plane. The hydrodynamic forces are then related to the body shape by using matched asymptotics.