The process for producing a sliced meat product includes the steps of partially cooking chunks of meat so that outside portions of the chunks reach temperatures above the temperature at which the meat is considered fully cooked while inside portions remain not fully cooked. One embodiment of the process includes slicing the meat chunks and adding to the slices sauce which is at a temperature above the temperature at which the meat is considered fully cooked, allowing the temperature of the meat and sauce to equalize at least to the extent that all meat reaches the temperature at which it is considered fully cooked, and portioning and packaging the product. Another embodiment of the process includes holding the partially cooked chunks of meat in a closed atmosphere so that the temperature of the meat chunks will at least partially equalize by the flow of heat from the higher temperature portions of the chunks to the lower temperature portions so that the entire chunks reach the temperature at which they are considered fully cooked. The chunks are then sliced, portioned, and packaged.