This paper presents the results of research on the development of a mathematical model of thermal desorption spectrometry with a surface ionization method for detecting molecules of organic substances, as well as an analysis of the capabilities of a thermal desorption spectrometer operating on the basis of this method. The mathematical model of the method was developed on the basis of the regularities of thermal desorption spectrometry, as well as the regularities of surface ionization of molecules of organic substances under non-stationary conditions. The spectrometer consists of a surface ionization detector and an evaporator of substances heated in a thermally programmed mode. The adjustment and selection of the operating mode of the spectrometer were carried out on the basis of the mathematical model of the method. The analytical capabilities of the spectrometer were studied by comparing the thermodesorption spectra of a mixture of chromatographically pure cannabinoids and an extract of the biological fluids of a marijuana user (blood, urine), as well as the spectra of chromatographically pure morphine and urine extracts of a heroin user. The results of the analysis showed the perspectives of the proposed method and instrument for the detection and analysis of drugs and psychotropic drugs in extracts of biomaterials of consumers of these substances without chromatographic separation. Keywords: biosamples of drug users, mathematical model of the method, thermal desorption spectrum, identification and quantitative analysis.