Results are reported for direct and inverse scattering of plane acoustic waves from sound-hard scatterers of arbitrary shapes in an infinite, homogeneous ambience. The direct problem is solved via a shape deformation technique which is valid for finite deformations. The resulting solution requires solving only a set of algebraic recursion relations, but neither integral equations nor Green’s function. The methodology has three essential features: all calculations refer exclusively to a known simple boundary Γs instead of the iteratively updated scatterer shapes; the Jacobian of the scattered field is evaluated by solving a series of Helmholtz’s equations (with different boundary data) in the region exterior to the simple shape Γs; and no ambiguity in the solution arises due to the interior eigenvalues. The inverse problem of recovering the scatterer boundary shape is solved by least square minimization using the Levenberg–Marquardt algorithm. Inversions of several two-dimensional shapes with varying degrees of complexity are reported. The procedures described generalize straightforwardly to transmission and three-dimensional problems.