Summary: Scattering of plane monochromatic acoustic waves on aplanar screen of arbitrary shape is considered (direct problem). The 2D-integral equation for the pressure jump on the screen is discretized by Gaussian approximating functions. For such functions, the elements of the matrix of the discretized problem take the form of a standard one-dimensional integral that can be tabulated. For regular grids of approximating nodes, the matrix of the discretized problem has the Toeplitz structure, and the corresponding matrix-vector products can be calculated by the Fast Fourier Transform technique. The latter strongly accelerates the process of iterative solution. Examples for an elliptic screen subjected to incident fields with various wave vectors are presented. The problem of reconstruction of the screen shape from the experimentally measured amplitude of the far field scattered on the screen (inverse problem) is discussed. Screens which boundaries are defined by a finite number of scalar parameters are considered. Solution of the inverse problem is reduced to minimization of functions that characterize deviation of experimental and theoretical amplitudes of the far field scattered on a screen. Local and global minima of these functions with respect to the screen shape parameters are analyzed. Optimal frequencies for efficient solution of the inverse problem are identified.