Application of the Tandem Accelerator Mass Spectrometer (AMS) in the radiocarbon dating of archaeologically derived materials has several primary advantages: 1) samples containing very small amounts of carbon may be dated; 2) actual archaeological artifacts may be dated without destruction; and 3) the method seems to produce dates as reliable as those obtained by earlier methods. In addition, the method will have some impact on archaeological method and theory. The archaeological dating process has been modeled in intricately theoretical ways to permit the association of independently-dated specimens with past cultural events. Owing to the previously undatable character of many archaeological specimens and artifacts such a multistage theory was necessary. Now that bones, seeds, ceramics, and other cultural materials can be dated directly by the AMS method dating theory may be simplified. Also, suites of AMS-derived carbon-14 dates may be used to cross-check other kinds of evidence and to study broad archaeological problems not resolvable using prior chronological methods. Finally, the capability of the AMS method to date very small samples will result in modifications in field collection techniques. Materials previously discarded as being insignificant will now become a focus of the archaeological search. In addition, microstratigraphic studies must be carried out and verified by cross-examination to ensure that the small samples collected have the provenience assigned to them. -- AATA