We present in this paper the Model Based System Synthesis (MBSS) approach for thedesign of complex systems that are correct by construction. Where the usual ModelBased System Engineering (MBSE) approach offers formalisms and tools to represent a candidate system, to analyze it, to simulate it and even to optimize it, MBSS proposes to represent the global design problem using a problem representation language and then to solve it by using adapted synthesis tools producing one or several solutions necessarily satisfying the expressed requirements. The two approaches are therefore complementary; the MBSS being more adapted to the preliminary design and system integration stages. After presenting the different categories of problems encountered in system design (sizing, configuration, allocation, architecture generation), MBSS and MBSE will be positioned in relation to each other. The main concepts of MBSS will be detailed in order to understand the specific representation needs of the approach. The structural and behavioral notions related to the sub-definite systems will be explained as well as the links to be established with the functional and non-functional requirements. The approach is illustrated using the DEPS design problem specification language and the DEPS Studio modeling and solving toolon a system design case study. The DEPS language combines structural modeling features specific to object-oriented principles and ontology definition capabilities for engineers with problem specification features from constraint programming. DEPS Studio is an integrated modeling and solving environment designed to model and resolve system synthesis problems. It allows the engineer to edit, compile, debug and solve problems expressed in DEPS. It integrates a mixed constraint programming solver. The approach can be applied on physical systems, software intensive or mixed systems (embedded or cyber-physical)