Hydrogen material science and engineering (including the ITER project) and connected technological problems need various construction materials with desired hydrogen permeability. Thermal desorption spectroscopy (TDS) is one of the experimental methods. The sample saturated by hydrogen is degassed in vacuum under monotonous heating. The desorption flux is measured using a mass spectrometer. These data gives information about interaction of hydrogen isotopes with the material. Such parameters of material as hydrogen diffusivity, solution and desorption rates, etc, need to be evaluated. In the paper we propose a distributed boundary-value problem of thermal desorption and a numerical method of the TDS spectrum. This method demands solving a nonlinear system of ordinary differential equations of relatively low order (compared with, e.g., the method of lines).