This study investigates the bearing capacity of rock masses and stability of slopes at the Subasi viaduct site which is a part of the improvement project of the Artvin-Hopa government highway between KM 6 + 500 and 13 + 787 in NE Turkey. The geotechnical studies were performed in three stages. Firstly, the bearing capacity of moderately weathered andesitic tuff was evaluated using the empirical equations. Secondly, the major principal stress and vertical displacement due to the viaduct and traffic loadings at the level of foundations were determined by the finite element method (FEM). The vertical displacement value and comparison of bearing capacity and major principal stress show that any problem is not expected at the viaduct site in terms of the bearing capacity. Finally, the stability of slopes at the viaduct site was investigated using kinematic, limit equilibrium, and finite element method-based shear strength reduction analyses methods. It was concluded that no discontinuity controlled failures at the slopes are expected. However, a circular failure is possible to occur at the face slope excavated in highly weathered andesitic tuff. After support application, the long-term stabilization of face slope has been achieved. Consequently, it is suggested that the empirical, analytical, and numerical methods should be combined for a more reliable construction design.