For a smooth convex obstacle the inverse problem of finding the surface of the obstacle from the knowledge of the scattering amplitude f(n,\(\nu\),k) at one large wavenumber \(k_ 0\) and n, \(\nu\) running through such a subset of the unit sphere \(S^ 2\) in \(R^ 3\) that the vector \(\ell =(n-\nu)| n-\nu |^{-1}\) runs through all of \(S^ 2\). The solution is based on the high-frequency asymptotics for the scattering amplitude. From this asymptotics one obtains the support function a(\(\ell)\) of the obstacle. If the support function is known then the parametric equation of the surface is given explicitly analytically. Stability of the solution with respect to small variations of the scattering amplitude is investigated and analytical estimates of the reconstruction error in terms of the error in the data and a priori assumptions about the Gaussian curvature of the obstacle are given. A detailed study of the problem is given by the author in [''Scattering by obstacles'', D. Reidel, Dordrecht (1986)]. The case when the obstacle is not convex is studied by \textit{H. D. Alber} and the author [Phys. Lett. 108, 238-240 (1985) and J. Math. Anal. Appl. 117, 570-597 (1986)].