In this doctoral dissertation, the issues related to the analysis of radioactive and nuclear material using gamma spectrometry as an analytical technique and also a technique that could potentially overcome the practical problems of measuring and analyzing the mentioned materials are discussed. The theoretical part of the dissertation includes the first, second and third chapters. In the first chapter, the basic definitions of nuclear forensics as a scientific-research discipline and concepts related to it are presented. The second chapter defines the place of nuclear forensics at the international level within international regulations and organizations. The third chapter provides an overview of the basic characteristics of nuclear and other radioactive materials that can be found outside of regulatory control. The experimental part of the doctoral dissertation begins with the fourth chapter, which deals with the used experimental techniques and methods of measurement and analysis of radioactive and nuclear material. This chapter presents gamma spectrometry as a method of nuclear forensics, as well as software packages that were used as a mathematical tool for the improvement and development of a non-destructive method of analyzing nuclear and other radioactive materials. The specifics of the samples that can be found in the field in terms of geometry, shape and density are part of the fifth chapter together with the results of the analysis. The obtained results indicate that both Angle and EFFTRAN software for efficiency transfer with adequate sample definition either in terms of geometry or composition and matrix gave satisfactory results which are consistent with the results obtained using the GEANT4 software package. It was also established that if in a given instance (criminal investigation) results are needed in a short time interval, the EFFTRAN software is a good tool for the ‘screening’ method, which gives quick results of activity concentration with a satisfactory level of confidence. Analyzes of the spectra of standard reference nuclear materials using the PC FRAM software package are given in the sixth chapter, where the basic observations related to the specifics of the analysis of this material are commented. In the conclusion, the advantages and disadvantages of the use of various mathematical calculations as an auxiliary tool in the analysis of the spectra of non-cylindrical samples of radioactive materials and the specifics of the analysis of nuclear materials are commented. Throughout the doctoral dissertation, an overview of nuclear forensics as a scientific discipline, as well as its place within national and international nuclear security, was given. In addition, it was shown how routine gamma spectrometric measurements can be used to measure specific materials for the needs of nuclear forensics while preserving the composition and shape of the sample being measured.