With an ever increasing urbanization and an ongoing climate change, new ways of thinking are required within urban drainage. Cities are becoming more dense and the resulting increase in impermeable surfaces often lead to urban flooding. Traditionally these issues have been tackled through the use of drainage pipe systems, but as the cityscapes expand these are becoming inadequate. A new way of sustainable urban drainage has emerged. This embraces the positive aspects of water in urban environments and relies on natural drainage mechanisms. One way in which such solutions are implemented is the use of grassed swales, which both infiltrate and create safe passageways for flooding events. These methods are, however, often designed using simplified methods that neglect infiltration and rapidly changing flow conditions. These are important aspects in evaluating grassed swales, making more detailed mathematical tools necessary. This research treats this issue in detail by investigating the use of dynamic wave equations combined with infiltration equations. A resulting numerical model for grassed swales is established and evaluated.