Contained within the Old English manuscript Exeter Cathedral Library MS. 3501, otherwise known as the Exeter Book, are 95 poetic riddles. These riddles have invited substantial study over the last 150 years, yet solutions to many of the riddles are still uncertain. This thesis examines two of these contested puzzles, Exeter Riddles 17 and 74. In his study, the author examines these two riddles through the method of Archaeo-Historicism. Such a method allows the investigation of the historical contexts surrounding each riddle, one that seeks clues outside of the verse. Once compiled, the historical evidence is used in conjunction with the clues offered in the riddles' texts themselves. Through this method, Chapter Two of the thesis solves Exeter Riddle 17 with the answer of "Viking Longship," and Chapter Three solves Exeter Riddle 74 with the answer of "Moon." Since the Exeter Book was likely created in the ninth or tenth centuries in England, it is likely that the volume's riddles reflect elements of life in the Anglo- Saxon world. Previous solutions to Riddles 17 and 74 however, have often failed historical tests of validity. The model of Archaeo-Historicism is thus useful in the search for evidentiary clues both inside and outside of the riddles' texts. In the concluding chapter, therefore, the author argues not only for the validity of his solutions, but also for the premise that solutions constructed from both literary and historical evidence are more viable than purely imaginative solutions.