The paper presents the results of the study of dynamic processes in the building of a historical architectural monument. A technical inspection of the building was performed and existing defects were identified. The analysis of potential sources of dynamic influences on the building is carried out. The technique of experimental researches is developed. The technique is based on a systems approach and involves the determination of dynamic parameters with the location of sensors directly on the individual elements of the studied structures. During the study, records of continuous fixation of the distribution of active oscillations of the structure were used. Numerical values of oscillation frequencies at different external sources are obtained. The nature of the distribution of amplitude values of oscillations in structures testified to the integrity of the structure as a single dynamic system. A comprehensive approach to solving the problem of modeling complex dynamical systems is considered. A mathematical model of a fragment of structures has been developed. The elements of the model create a multilayer structure with variable elastic characteristics. The results of numerical studies of the behavior of structures, taking into account the presence of peeling plaster, indicate a significant increase in natural frequencies of oscillation (up to 10 times), taking into account the partial lack of adhesion between plaster and load-bearing structures. As a result of separation, the plaster begins to work as a separate element with its own frequency with which it can resonate with other vibrating sources. The method of experimental-numerical analysis of the object is offered. This approach is based on the premise of determining the dynamic parameters of the interaction of subsystems with each other. The obtained numerical values of dynamic parameters will be used in further monitoring of the investigated building, on the basis of which it is possible to predict possible scenarios of behavior of structures over time. The research results can be used in the restoration process for optimal fixing of plaster fragments and avoidance of resonant phenomena in operation on the basis of detailed local mathematical models.