El Mirador de los Túneles is a tube-shaped volcanic cave with a sinuous structure in the Galápagos Islands formed due to cooled near-surface lava flows. Since this natural formation is considered a tourist site, a large number of people frequent it daily; however, its safety conditions have not yet been defined by a comprehensive geotechnical study. In this research, a stability analysis was carried out by combining both empirical methodologies based on geomechanical classifications using Barton’s Q Index and the recently created Cave Geomechanical Index (CGI), and numerical modeling through the finite element method. In addition, three-dimensional modelling was performed using the remote photogrammetric technique Structure from Motion (SfM) to create the numerical calculation sections and dimensions of the different critical parts of the cave. The results of the analysis showed that there is evidence of instability and subsidence along the tunnel. Furthermore, the geotechnical parameters obtained from the different methods complemented each other, resulting in more realistic engineering representation of the subsurface environment. Finally, a graph showing the two empirical methodologies Barton’s Q Index and CGI, with the addition of the Factors of Safety (FoS) obtained from the modeling is presented.