Variations of reflection amplitude with offset and azimuth are sensitive to the presence of natural and induced fractures. We tested inversion for fracture compliance matrix components from wide azimuth noisy synthetic PP-reflection data. The model was a fractured reservoir with monoclinic symmetry, formed by two sets of vertical asymmetric fractures embedded in a VTI background. The fractures (joints) were assumed to be vertical, with noncircular shape and/or with asymmetric shear compliance. Results of synthetic inversion showed that an incorrect assumption about fracture shear symmetry (e.g., treating asymmetric fractures as rotationally invariant fractures) can cause considerable error in estimation of the fracture compliance matrix. Components of effective second- and fourth-rank fracture compliance matrices for a medium with monoclinic symmetry (which takes into account layering and multiple fracture sets) can be used as attributes related to the characteristics of the fractured medium. Monte Carlo simulation was used to test the effect of uncertainties in the a priori information (about background VTI parameters of unfractured rock), as they affect inversion for these attributes. According to this analysis, the direction of fast shear-wave polarization was inverted robustly in the Monte Carlo simulation. Although the average values of the components of fracture compliance matrices obtained from Monte Carlo simulation were in agreement with the actual values used for forward modeling, individual values obtained in Monte Carlo simulation were sensitive to uncertainties in the background properties in general. Because the elastic properties of background VTI media without fractures (or other azimuthally variable features) do not cause azimuthal changes in reflection coefficient variation with offset, simultaneous inversion for background properties and fracture tensor components require additional constraints.