The results of direct and inverse scattering of plane acoustic waves from penetrable and impenetrable objects are reported here. It is assumed that the scatterer boundary is a superposition of an arbitrary deformation on an underlying simple geometry. The direct problem is solved via the Padé extrapolation of the boundary variations. This results in solving only certain algebraic recursion relations and requires neither Green’s function nor integral representations. The inverse problem of recovering the obstacle’s shape and material parameters from the far-field scattering data is solved by Gauss–Newton minimization. The calculation of the scattered field and its Jacobian involves no more than solving a series of Helmholtz scattering problems in the same domain, namely, exterior to the simple shape instead of the iteratively updated deformed surfaces, leading thereby to substantial computational simplifications. Moreover, since no integral equation is used, the ambiguity in the solution because of the interior eigenvalues does not arise. Several two-dimensional obstacles of various shapes are inverted for their boundaries as well as their material parameters of mass density and wave number. Finally, the procedures described can be extended straightforwardly to transmission and three-dimensional problems.