The present disclosure relates to surgical fastener applying apparatus, and the application of variable compression to tissue. More specifically, the presently disclosed surgical fastener applying apparatus act to limit the flow of blood through tissue immediately adjacent a cut-line formed therein to effectuate hemostasis, while maximizing the flow of blood through tissue more removed from the cut-line to limit unnecessary necrosis. In one embodiment, a surgical fastener applying apparatus is disclosed having a tool assembly coupled to a distal end thereof with first and second jaws respectively including an anvil and a surgical fastener cartridge. The surgical fastener cartridge includes, among other things, a hemostasis member that is configured to apply at least two different compressive forces to tissue clamped between the first and second jaws of the tool assembly.