Nuclear medicine (NM) is a medical discipline that primarily involves clinical procedures in which a small amount of a compound, labelled with a radionuclide is administered to the patient’s body to obtain diagnostic information about various disorders and diseases. The main imaging device in nuclear medicine imaging techniques is a gamma camera. Monte Carlo (MC) simulations play an important role in nuclear medicine because, unlike measurements, simulations can test the influence of certain parameters on the image quality and quantitative accuracy which is experimentally impossible or significantly limited. Examples of the use of MC simulations are the optimization of correction schemes for scattered radiation in single photon computed emission tomography and its use in the design of quantitative imaging studies for radionuclide radiotherapy dosimetry. In this thesis, the MC program package SIMIND was used to study the characteristics of the energy spectra of three sources of radionuclides 99m^Tc, 131^I and 123^I, which are intensively used in imaging procedures and radionuclide therapy. The simulated energy spectra of the sources were compared to the measured ones, obtained with the dual-headed Symbia T gamma camera (Siemens, Germany), with and without a collimator. The measurements were carried out at the Department of Oncology and Nuclear Medicine, KBC Sestre milosrdnice in Zagreb. In addition to comparing the general features of the spectra obtained by simulations, the full widths at half maximum of the most significant photopeaks in the spectra were determined with different assumptions about the shape of the function that describes the dependence of the peak width on photon energy. The investigation shows a good agreement between the values of the full widths at half maximum of the peaks in the measured and simulated intrinsic energy spectra, up to approximately 160 keV, for the theoretical and the fitted energy resolution model. The theoretical model assumes the largest contribution to the FWHM from the statistical variation of the output pulse amplitude of the detector system, originating from the number of photoelectrons released from the photomultiplier photocathode, while the proposed fitted model uses a modified nonlinear function of the FWHM dependence on the energy of the incident photon. At higher photopeak energies, the fitted model proved to be more accurate than the theoretical one. Accurate knowledge of the full width at half maximum of the photopeaks in energy spectra significantly affects the knowledge of the exact content of the energy window from which NM images are formed, and the implementation of algorithms for scattered radiation correction that provides superior accuracy in imaging methods, especially important for individualized dosimetry of targeted radionuclide radiotherapy.