This paper presents a proposed method for seismic assessment of masonry heritage structures based on the modern Eurocode 8—Part 3 and Greek Code for Interventions of Masonry Structures regulations. The methodology is presented through the study of a three-story building with stone and brick masonry, floors with metal and timber beams and a timber roof. The main objects of this study include the selection of analysis method combined with the method of evaluating the load—bearing capacity of the structural elements of the building. This process together with the defined Performance Levels—a parameter introduced by the modern codes—is particularly important, as it determines the level of the applied seismic demands. Considering the framework defined by the code regulations, the developed numerical models using Finite Element Method (F.E.M.) are formed with shell and frame elements. The seismic assessment is conducted through Equivalent Static Analysis, calibrated based on Response Spectrum Analysis. Both Load-based and Displacement-based assessments are applied. Displacement-based method allows the nonlinear response of the masonry components, leading to a less conservative evaluation and limiting the extent of the required strengthening schemes. This method could be applied especially in heritage buildings, where extended interventions are not recommended.