We analyze the modal response of the top plates of archtop guitars using free boundary conditions. Starting from the three-dimensional scan of a real archtop guitar, we build a mesh of its top plate using a non-invasive process. Once the mesh of the plate is built, we compute its vibrational response by finite element method simulations and perform many different analyses. The outer surface of the mesh matches the scan, while we retain the freedom to control the shape of the inner surface. This way we can change some of its aspects (e.g., thickness distribution) depending on what we intend to study. We investigate the similarities of its mode shapes with those of similar instruments (e.g., violin and classical guitar), analyze the carving process of the plate's inner surface and study the influence of resonant holes on its final vibratory response.