Modern cities are full of complex and substantial engineering structures that differ by their geometry, sizes, operating conditions, and technologies used in their construction. During the engineering structures’ life cycle, they experience the effects of construction, environmental, and functional loads. Among those structures are bridges and road overpasses. The primary reason for these structures’ displacements is land subsidence. The paper addresses a particular case of geospatial monitoring of a road overpass that is affected by external loads invoked by the construction of a new subway line. The study examines the methods of machine learning data analysis and prediction for geospatial monitoring data. The monitoring data were gathered in automatic mode using a robotic total station with a frequency of 30 min, and were averaged daily. Regression analysis and neural network regression with machine learning have been tested on geospatial monitoring data. Apart from the determined spatial displacements, additional parameters were used. These parameters were the position of the tunnel boring machines, precipitation level, temperature variation, and subsidence coefficient. The primary output of the study is a set of prediction models for displacements of the overpass, and the developed recommendations for correctly choosing the prediction model and a set of parameters and hyperparameters. The suggested models and recommendations should be considered an indispensable part of geotechnical monitoring for modern cities.