The present disclosure generally relates to flexible drainage trap assemblies and methods for constructing and installing such drainage traps. In one exemplary embodiment, a flexible drainage trap assembly includes a plumbing fixture connector, a discharge joint, and a trap portion connecting the plumbing fixture connector and discharge joint. The trap portion is shaped in such a way that it is operable to retain a pool of water inside the trap portion. The disclosed flexible drainage assemblies include a flexible portion that has a substantially smooth inner surface.