An end effector for use with a circular surgical stapling instrument, said end effector comprising: a staple cartridge, comprising: a cartridge body comprising an annular array of staple cavities; staples removably stored in said staple cavities; a firing drive configured to eject said staples from said staple cavities; and an annular cutting member, wherein said annular cutting member is surrounded by said annular array of staple cavities; and an anvil, comprising: a tissue compression surface; forming surfaces configured to deform said staples; and a tissue support, wherein said anvil is movable toward said cartridge body to compress tissue between said cartridge body and said tissue support, and wherein said cutting member is configured to incise the tissue and said tissue support during a cutting stroke of said cutting member, said tissue support comprising: an annular central aperture; a first annular wall defining said annular central aperture; a second annular wall; a top wall; a bottom wall; and lateral sidewalls connecting said first annular wall and said second annular wall and extending between the top wall and the bottom wall, wherein said lateral sidewalls comprise an annular array of lateral sidewalls, and wherein said tissue support further comprises an annular array of cavities defined within said annular array of lateral sidewalls, wherein said tissue support is configured to snap when said cutting member applies a load to said tissue support, said end effector being characterized in that the tissue support comprises a rigid polygonal cross-section, wherein said first annular wall is shorter than said second annular wall, and wherein the top wall comprises an inclined portion which extends transversely to the bottom wall. a staple cartridge, comprising: a cartridge body comprising an annular array of staple cavities; staples removably stored in said staple cavities; a firing drive configured to eject said staples from said staple cavities; and a cartridge body comprising an annular array of staple cavities; staples removably stored in said staple cavities; a firing drive configured to eject said staples from said staple cavities; and an annular cutting member, wherein said annular cutting member is surrounded by said annular array of staple cavities; and an anvil, comprising: a tissue compression surface; forming surfaces configured to deform said staples; and a tissue support, wherein said anvil is movable toward said cartridge body to compress tissue between said cartridge body and said tissue support, and wherein said cutting member is configured to incise the tissue and said tissue support during a cutting stroke of said cutting member, said tissue support comprising: an annular central aperture; a first annular wall defining said annular central aperture; a second annular wall; a top wall; a bottom wall; and lateral sidewalls connecting said first annular wall and said second annular wall and extending between the top wall and the bottom wall, a tissue compression surface; forming surfaces configured to deform said staples; and a tissue support, wherein said anvil is movable toward said cartridge body to compress tissue between said cartridge body and said tissue support, and wherein said cutting member is configured to incise the tissue and said tissue support during a cutting stroke of said cutting member, said tissue support comprising: an annular central aperture; a first annular wall defining said annular central aperture; a second annular wall; a top wall; a bottom wall; and lateral sidewalls connecting said first annular wall and said second annular wall and extending between the top wall and the bottom wall, an annular central aperture; a first annular wall defining said annular central aperture; a second annular wall; a top wall; a bottom wall; and lateral sidewalls connecting said first annular wall and said second annular wall and extending between the top wall and the bottom wall, wherein said lateral sidewalls comprise an annular array of lateral sidewalls, and wherein said tissue support further comprises an annular array of cavities defined within said annular array of lateral sidewalls, wherein said tissue support is configured to snap when said cutting member applies a load to said tissue support, said end effector being characterized in that the tissue support comprises a rigid polygonal cross-section, wherein said first annular wall is shorter than said second annular wall, and wherein the top wall comprises an inclined portion which extends transversely to the bottom wall.