One of the technological challenges for hydrogen materials science (including the ITER project) is the currently active search for structural materials with various potential applications that will have predetermined limits of hydrogen permeability. One of the experimental methods is thermal desorption spectrometry (TDS). A hydrogen-saturated sample is degassed under vacuum and monotone heating. The desorption flux is measured by mass spectrometer to determine the character of interactions of hydrogen isotopes with the solid. The paper presents a distributed boundary-value problem of thermal desorption with dynamical boundary conditions and a numerical method for TDS spectrum simulation, where only integration of a nonlinear system of low order (compared with, e.g., the method of lines) ordinary differential equations (ODE) is required. It has been suggested dissolution and desorption coefficients estimation method in a real dynamic interaction of surface and diffusion processes without the artificial division of studies into diffusion limited regime (DLR) and surface limited regime (SLR). This work is supported by the Russian Foundation for Basic Research (project № 15-01-00744).