The application of infiltration basins and tanks is one of the primary means of sustainable stormwater management. However, the methods currently used to size these facilities do not take into account a number of parameters that have a significant impact on their required capacity. In light of this, the aim of this research was to develop a new method for selecting the geometry of the infiltration basins and tanks. Its application in the initial phase of designing stormwater management systems will allow assessing the validity of using such facilities in a given catchment area. This paper also presents the results of local and global sensitivity analyses examining how changes in individual design parameters influence stormwater infiltration facilities. The effectiveness of the developed model was evaluated through the example of a real urban catchment. The study was based on a hydrodynamic analysis of more than 3000 model catchments. The research plan was developed using Statistica software. On the other hand, the analysis of the results of hydrodynamic simulations was made possible through the use of artificial neural networks designed using the Python programming language. The research also confirmed that parameters such as the total catchment area, the percent of impervious area, and the type of soil within the catchment are crucial in the design process of these facilities. The results of this research can be considered when designing infiltration basins and tanks under Polish conditions. The described algorithm can also be used by other researchers to develop similar models based on different rainfall data. This will contribute to increasing the safety of urban infrastructure.