Packing sheet materials into cylinders and prisms using Origami-based approaches (Soft Origami or traditional Origami) is of interest in fields where sheet materials need folded into cylinders or prisms. Fully-dense packing has application in fields where a sheet material is to be folded with minimal gaps into a cylinder or prism. Partially-dense packing is applicable to fields where gaps are required between packed surfaces or where hollow volumes are to be filled, such as in fluid filter design. Soft Origami is explored as a method for folding soft-sheet materials into fully-dense cylinders. Two fold patterns, the "flasher'' and the "inverted-cone fold,'' are explored for packing soft-sheet materials into cylindricals. An application to driver's side automobile airbags is successfully performed, and deployment tests are completed to compare the influence of packing method and origami pattern on deployment performance. In total, two origami patterns and six packing methods are examined for folding soft-sheet materials into fully-dense cylindrical prisms, and it is shown that modifying the packing method impacts deployment performance. A special case of the Miura-ori, the ninety-degree case, is briefly explored as a traditional Origami method for packing arbitrary-shaped sheet materials into fully-dense arbitrary prisms. Examples are shown and it is concluded that this pattern can be used to configure a large number of fully-dense packed prisms with configurable characteristics.Finally, patterns that fold into partially-dense cylindrical prisms are examined using traditional Origami approaches and their efficiency compared. Efficiency is defined as the ratio of the surface area of a pattern compared to an idealized high-surface-area model. Patterns include traditional (non-Origami-based) fluid filter patterns (the Basic Pleat and M-pleat) and cylindrical Origami patterns (the Accordion and Kresling). An offset crease method is used to modify the Accordion and Kresling Origami patterns so the comparison is objective. Results are presented that determine which individual pattern variations have the highest efficiency at different outside-to-inside diameter ratios. Ranges over which each pattern is most efficient are presented. It is concluded that based purely on geometry, the M-pleat provides the highest overall efficiency, but depending on other factors each pattern is viable for different purposes.