This article discusses the development of methods for solving coefficient inverse problems of ultrasonic tomography in application to non-destructive testing of thin plates using Lamb waves. The problem of ultrasonic tomographic diagnostics is formulated as a coefficient inverse problem of reconstructing the thickness of the plate as a function of two coordinates. Iterative methods for approximate solution have been developed using the gradient descent method to minimize the discrepancy between the experimental data and the data computed in the scalar wave model at the detectors. The experimental data is simulated by solving the direct problem in 3D elastic vector model. The effectiveness of the proposed algorithms is illustrated on model problems. High-performance computing nodes of a supercomputer complex are used as a computing platform.