Total reduplication is common in natural language phonology and morphology. However, formally as copying on reduplicants of unbounded size, unrestricted total reduplication requires computational power beyond context-free, while other phonological and morphological patterns are regular, or even sub-regular. Thus, existing language classes characterizing reduplicated strings inevitably include typologically unattested context-free patterns, such as reversals. This paper extends regular languages to incorporate reduplication by introducing a new computational device: finite state buffered machine (FSBMs). We give its mathematical definitions and discuss some closure properties of the corresponding set of languages. As a result, the class of regular languages and languages derived from them through a copying mechanism is characterized. Suggested by previous literature, this class of languages should approach the characterization of natural language word sets.