A method is presented for the reconstruction of inhomogeneous surface impedance of a two-dimensional (2D) cylindrical object of slightly varying arbitrary shape located over a perfectly electric conducting (PEC) plane. The method is an extension of the one given previously (Akduman I and Kress R 2003 Radio Sci. 38 1055). By the use of a single layer potential representation of the scattered field the problem is first reduced to the solution of an ill-posed integral equation which can be treated by truncated singular value decomposition (TSVD). Then the field itself and its normal derivative on the boundary of the object, which are required for the evaluation of the surface impedance, are obtained by the use of jump relations through the Nystrom method. Since the reconstruction of the surface impedance from the field and its normal derivative is ill-posed, a regularized solution in the sense of least squares is applied. By considering the relation between the shape of a PEC object and its equivalent one in terms of surface impedance, it is shown that the method can also be used in the shape reconstruction. The numerical implementation shows that the method is capable of reconstructing the surface impedance as well as shape even with aspect limited data. This is due to the fact that the PEC plane has a mirror effect on the measured data which corresponds to full view configuration as in the case of objects located in an infinite medium.