The authors examined the problem of the spread of drug abuse and describe a research procedure based on the method of cognitive modeling. To achieve this, the authors formulated the problems that are solved through cognitive modeling, which includes the following stages: outlining the problem field, building a cognitive map in the form of an orgraph, coordinating expert evaluations of the mutual impact of various factors, working out expert rules based on the cause-and-effect speculations, and conducting an imitation experiment. The first stage of cognitive modeling included an overview of research publications on the problem, which allowed the authors to identify the set of contributing factors. Stages of cognitive modeling were used to build a cognitive model «The spread of drug abuse» with such influencing factors as «the condition of the dwelling and utilities sphere», «professional occupation», «degree of the society’s criminalization», «organization of leisure activities and cultural work for the population», «prevention measures». The target factor was «the spread of drug abuse». The adequacy of the developed cognitive structure was verified by the systemic feature of «sensitivity» in the imitation experiment that recreates some semblance of reality in laboratory conditions. Analytical procedures were used to determine the expert evaluations of the mutual impact of factors and to work out expert rules. A cognitive map was developed in the form of a weighed orgraph, which was viewed as the framework of the problem where it was possible to observe the changes in the overall holistic situation by influencing its various points. The imitation experiment was conducted using Microsoft Excel, and its results agree with the logics of speculations. It is stated that although the simplified cognitive map includes five factors that influence the problem, increasing their number to build a more large-scale version of the cognitive model will contribute to deeper and more comprehensive research of the problem. The presented model is a promising area for the application of modern methods of researching the spread of drug abuse and spread of crimes in the sphere illegal drug trade with the use of Big Data technology.