In 1992 the Ulysses spacecraft discovered periodic dust streams escaping from the Jovian system. In 2000, M. Horanyi proposed that the escaping dust streams are not a particular feature of the Jovian system and predicted streams of dust particles escaping from Saturn as well. In this work we apply an analytical model, already applied to Jupiter (Maravilla et al., 1995), in order to analyze two possible and different sources: On the one hand the satellites Dione, Helene, Rhea and Enceladus; on the second, the A-ring outer boundary. Additionally, some general properties of the dust particles that compose these Saturnian streams, such as their radii and escaping speeds, are drawn.