A calculation method for accurately computing the displacement, image stress, and image energy induced by defects, such as cavities, precipitates, finite dislocation segments, and dislocation loops, in a free-standing anisotropic thin crystal film is presented. The anisotropic image stress is derived in the Fourier space from the standing Christoffel stress equilibrium equation for anisotropic materials, relying on the elastic parameters, the crystallographic orientation of the film and the considered defect. The image stress corresponds to the traction stress field, describing the stress field at the free surface. The latter is the stress induced by the same defects in an infinite medium evaluated at the location of the free surface. This method is applied to pure bcc Fe semi infinite single crystals and thin crystal films. The calculation results show that a stronger image stress induced in-plane and out-of plane displacement difference is produced with the anisotropic elasticity for bcc Fe, relative to the isotropic case, calculated by either Voigt or Reuss methods. It confirms that anisotropy has a strong influence on the image stress induced 3D displacement fields. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4764341]