In this paper, we present a method for the solution of a location and shape reconstruction problem related to sound-soft obstacles buried in arbitrarily shaped penetrable cylinders in two dimensions. The direct problem considered here is to obtain the scattered near/far-field in the case of a single time-harmonic acoustic plane wave insonification. The aim of the inverse problem is to find the shape as well as the location of the buried scatterer from the limited/full aperture measurements of the scattered field via Newton iterations. Both for the direct and inverse scattering problems, different potential (layer) approaches are used to derive a system of boundary integral equations. The integral equations are evaluated by using Nystrom and collocation methods. Moreover, in order to obtain a stable solution of the first kind of Fredholm-type integral equations Tikhonov regularization is employed. We test the applicability and the effectiveness of the inversion algorithm also with noisy limited far-field data and obtain satisfactory numerical results as illustrated in the last section.