The metal strung harp indigenous to Ireland and Scotland from the Medieval period to the end of the 18th century was widely admired throughout its time period, and is now an important part of the cultural and musical heritage of both of these countries. This type of harp, known as the 'Irish harp', cláirseach, or clàrsach, currently has 18 known surviving instruments, including two sets of fragments. All of these harps are now too fragile to be played, therefore musicians and audiences wishing to explore the performance practice and repertory associated with them must rely on faithful replicas. The extensive knowledge and understanding of the construction of the surviving harps that is crucial to building these replica instruments is currently very limited, however. Although harps of this type enjoyed a long period of use dating back to the Medieval period, most surviving instruments post-date the beginning of the 17th century. Two harps belonging to the National Museum of Scotland, the 'Queen Mary' and 'Lamont', generally dated to circa the 15th century, are understood to be two of the oldest extant examples, making a study of their construction of particular interest. This dissertation presents the results of a comprehensive study of the construction of these two harps. A methodology was developed to address the issue of their uniqueness and fragility by combining the techniques used for non- and minimally destructive analysis of archeological artefacts with non-invasive medical diagnostic imaging. This study has utilized CT-scanning to provide three-dimensional radiography of each harp; XRF and SEM-EDX analysis to identify woods, metals, and pigments; photography and microscopy to record the decorative work, visible damage, repairs, and modifications; and a visual examination to assess the current state of each harp and to identify areas of interest for further analysis. The CT scanning was conducted at the Clinical Research Imaging Centre of Queen's Medical Research Institute, and the remainder of the analysis was conducted at the National Museums Scotland Collections Centre. Staff at both centres kindly facilitated the acquisition of the data for this study. Part I of this dissertation discusses the stringing of the instruments, presenting materials analysis of wire fragments, analysis of the effect of damage to the frames on the length and number of strings, and proposed reconstructions of the 'as-built' string lengths. Possible solutions for the pitch and gamut of each harp are also discussed. The construction of the harps is discussed where it is relevant to understanding the stringing. Part II presents a general discussion of the construction of each harp, including materials, decorative work, modifications, and signs of wear. This section also discusses evidence that may help establish dates of construction and timelines of modifications. Diagrams showing the dimensions of each harp are also presented. The implications of the results of this study for current understanding of these harps are discussed in detail and the methodology employed is discussed in terms of its applicability to future research of other surviving instruments.