Summary form only given. Two approaches are being used in non-thermal atmospheric pressure plasma treatment of human tissue and sterilization surfaces. In the first, the plasma is produced remotely and its afterglow is delivered in a plume to the tissue. When plasma jets are used, the sterilizing or therapeutic effects are likely produced by relatively long-lived neutral species and radicals as most of the charged particles do not survive outside the plasma generation region. These jets are usually operated with a few percent of molecular gases such as O2. in helium to avoid plasma instabilities. The resulting reactive oxygen species (ROS) are delivered to the tissue where some amount of energy transfer from metastable states may occur in addition to chemical processes. The jets interacting with air may also generate fluxes of reactive nitrogen species (RNS). In the second approach, plasmas are generated in direct contact with living tissue or bacteria. When dielectric barrier discharges (DBDs) are used for this purpose, the plasma source typically contains the powered electrode while the tis sue is the counter electrode. The direct method differs from the indirect technique by delivery of ions and photons to the surface with fluxes orders of magnitude larger. The charging of the tissue (or bacteria) can produce electric fields large enough for electroporation. In this talk, we will discuss results from a computational comparison of the treatment of liquid covered wounds by di electric barrier discharges and plasma-jets. The interaction of single and multiple filaments in DBDs with the wounds as well as different regimes of plasma-jet operations will be con sidered. The production and diffusion of ROS into the blood serum, to blood platelets and to the underlying cells will be discussed. The studies will be performed using a computer model which solves for charged particle, neutral and photon fluxes while solving Poisson's equation, and resolving spa- ial scales on reactor-to-cellular levels.