A relevant task of the single-photon emission computer tomography (SPECT) combined with computer tomography (CT) is development of quantitative assessment of generated images of pathological regions and optimization of a protocol of the procedure for patient examination using this method. Solution of these tasks requires a great number of the studies. Development of the mathematical modeling method is a relevant task in the field of nuclear medicine concerning ethical limitations due to a radiation load. In order to solve this task, it is necessary to create the models of the "virtual patients", which describe distribution of a delivered radiopharmaceutical in the organs and the tissues and its accumulation in pathological foci. The present paper proposes approaches for creating the mathematical models of the patients (phantoms) to study diagnostics accuracy of the SPECT method combined with computer tomography (SPECT/CT). Two approaches for creating the models of the"virtual patients" have been developed. The first approach Constructive Solid Geometry (CSG) based on the equations of analytical geometry constructs models of an average patient. The second approach creates the so-called "digital twins" based on segmentation of clinical SPECT/CT images of real patients. The CSG phantoms were successfully applied in the simulation modelling directed at the studies of and solving the general problems of SPECT/CT visualization. These problems include the studies of optimum parameters of the data collection protocol and a problem of a false apical defect in the nuclear cardiology.The "digital twins" can the most accurately model clinical cases and evaluate errors on reconstructed images. Both the approaches to creation of the models of the "virtual patients" have their own niche of research. The problems to be solved by a large number of tests with varying several anatomical parameters (for example, a patient habitus, angular orientation, the thickness of the walls of and the size of myocardium of left ventricle) are the most suitably studied using the geometrical CSG models.The "digital twins" shall be used when studying real clinical cases as well as for verification of solutions and conclusions obtained in the studies using the CSG models. Keywords: phantom, single-photon emission computer tomography, computer tomography, modeling.