Rock fractures in the subsurface typically have apertures less than a wavelength of the dominant frequency of the GPR signal, thus generating complex reflectivity pattern. The resulting reflectivity is however useful as it depends on the fracture aperture and dielectric permittivity of the filling material. AVA analysis relates amplitude variations with increasing incidence angles and seeks to characterize interfaces and layers. In this paper, I present theoretical analysis of the AVA behaviour of thin fractures, assessing the sensitivity to fracture aperture and fill characteristics. The magnitude and curvature of the AVA curves depend on the fracture aperture and fill permittivity suggesting that fracture aperture and fill permittivity can be obtained from field measurements. Amplitude data for AVA analysis is collected in the field through CMP surveys. Converting these amplitude data for AVA analysis requires some careful but simplifying assumptions on the system under investigation, applying some amplitude corrections and offsets need to be converted to incidence angles. Fracture aperture and fill permittivity can then be constrained by fitting theoretical AVA curves for various fracture models to a field derived AVA curve.