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This study explores the methods of wave tomography in application to the problem of reconstructing the wave velocity inside flat objects. Numerical simulations were carried out for 2D inverse problems that represent nonde-structive tomographic imaging of welded joints in metal samples. Tomographic diagnostic methods employing transducer arrays are proposed for imaging flat objects that are accessible only from a single side. In this case, the waves reflected from the flat bottom of the inspected object can be used for sounding. The thickness of the flat object is assumed to be known. The multistage iterative method made it possible to effectively solve nonlinear inverse problems of ultrasound tomography and to reconstruct the sound speed images of simulated test objects, small cracks and cavities. The gradient method works best if the contrast in sound speed is low. Acoustic and geometric parameters of the simulations correspond to a real experiment. Numerical simulations were performed on supercomputer. Capabilities of CPU and GPU computing platforms for solving inverse problems of ultrasound tomography in non-destructive testing are discussed.