One of the main concerns of software engineering is the automation of reuse in order to produce high quality applications in a faster and cheaper manner. Model-Driven Software Product Line Engineering is an approach providing solutions to systematically and automatically reuse generic assets in software development. More specifically, some solutions improve the product line core assets reusability by designing them according to the Model-Driven Architecture approach. However, existing approaches provide limited reuse for platform-specific assets. In fact, platform-specific variability is either ignored or only partially managed. These issues interfere with gains in productivity provided by reuse. In this paper, we first provide a better understanding of platform-specific variability by identifying variation points in different aspects of a software based on the well-known "4+1" view model categorization. Then we propose to fully manage platform-specific variability by building the Pl atform-Specific-Model using two sub-models: the Cross-Cutting Model, which is obtained by transformation of the Platform-Independent Model, and the Application Structure Model, which is obtained by reuse of variable platform-specific assets. The approach has been experimented on two concrete applications. The obtained results confirm that our approach significantly improves the productivity of a product line.