During the last decades, many destructive earthquakes occurred in Algeria, particularly in the northern part of the country (Chlef (1980), Constantine (1985), Tipaza (1989), Mascara (1994), Ain-Benian (1996), Ain Temouchent (1999), Beni Ourtilane (2000), and recently $Boumerd{\acute{e}}s$ (2003), causing enormous losses in human lives, buildings and equipments. In order to reduce this risk and avoid serious damages to the strategic existing buildings, the authorities of the country, aware of this risk and in order to have the necessary elements that let them to know and estimate the potential losses in advance, with an acceptable error, and to take the necessary countermeasures, decided to invest into seismic upgrade, strengthening and retrofitting of those buildings. To do so, seismic vulnerability study of this category of buildings has been considered. Structural analysis is performed based on the site investigation (inspection of the building, collecting data, materials characteristics, general conditions of the building, etc.), and existing drawings (architectural plans, structural design, etc.). The aim of these seismic vulnerability studies is to develop guidelines and a methodology for rehabilitation of existing buildings. This paper presents the methodology, based on non linear and seismic analysis of existing buildings, followed in this study and summarizes the vulnerability assessment and strengthening of one of the strategic buildings according to the new Algerian code RPA 99/version 2003. As a direct application of this methodology, both, static equivalent method and non linear dynamic analysis, of composite concrete masonry existing building in the city of "CONSTANTINE", located in the east side of ALGERIA, are presented in this paper.