Farm tourism is often considered a form of tourism whose main characteristic is sustainability. Nevertheless, the existing literature also provides a partial approach, where the development of farm tourism is analyzed within the context of sustainable development and crisis situations, such as the COVID-19 pandemic. The aim of the paper is to analyze environmental, social, and economic factors as vectors for the sustainable development of farm tourism by applying a specially designed SFT model. An empirical study was carried out on a sample of nine farms in the peri-urban area of the city of Novi Sad (the Republic of Serbia). Sustainable development was analyzed using dynamic social, economic, and environmental indicators with the aim of finding a model that could be used to ensure more stable economic income for the population, social equality, and environmental protection. By applying the SFT model, it was determined that the current position of farm tourism is not fully compliant with the aims of sustainable development due to its clearly dominant economic dimension and less developed social and environmental sustainability. The results were further analyzed with the aim of achieving a balanced development of farm tourism, which needs to be based on the continued application of the concept of sustainability. The results could be used by public and private institutions in the tourism sector, as well as creators of legal regulations and strategies in the field of sustainable and rural tourism, with the aim of further developing and improving its sustainability.