This thesis presents the development of models for the simulation and optimization of the design of a planar solid oxide fuel cell (SOFC) stack. Fuel cells produce electric power directly from a fuel by electrochemical reactions. The high efficiencies demonstrated make them a promising technology for energy conversion. The main challenges lie with reliability and cost reduction. Some applications demand at the same time strong requirements on the compactness of the system and its ability to load following. The models have been developed to represent the novel stack proposed by HTceramix SA (Yverdon, Switzerland) which is tested and partly developed at the Laboratoire d'Energétique Industrielle (LENI). The model has been created in a way which allows its use for design optimization: this requires detailed and validated outputs to gain insight in the behavior of a new stack design and computational efficiency to allow sensitivity studies and optimization. Electrochemistry, mass and heat transfer phenomena are combined with a 2D fluid motion description to obtain a generalized model which can be applied to a large range of geometries. An efficient stack modeling approach is proposed. Validation of the model has been carried out with measurements and a 3D computational fluid dynamics model. A methodology based on parameter estimation has been used to identify kinetic parameters and other uncertain parameters. Local temperature measurements and a local current density measurement have been performed and also used for model validation. The 2D model has been successfully validated showing good agreement with both the experiments and the detailed 3D model. Simulation of the novel stack geometry (counter-flow) has allowed to identify the main problems arising from this compact geometry where the non-homogeneous velocity field creates stagnant zones which limit the operation at high efficiency. The simulated temperatures are characterized by important gradients and excessive level values (>850°C) for an intermediate temperature SOFC (700-800°C). This motivated to work on an alternative geometry, which based on simulation results, solves most of the problems previously identified. The thesis presents several examples of the influence of design on the system performance and reliability. Transient simulations have been performed and the design choice had only a small impact on the transient behavior which presents intrinsically an important thermal inertia. On the contrary, degradation behavior is dependent on the design. Stack degradation has been simulated by including the metal interconnect degradation into the stack model. The approach has allowed to identify a new criterion to express degradation consistently for different test conditions. To assist stack design, new approaches are necessary. The geometry of a stack was initially determined by a number of decision variables (such as cell area, thickness of the channels and interconnects) on which extensive sensitivity analysis were conducted. This method is of limited use as each of the objectives on stack design led to different solutions. To overcome this limitation, multi-objective optimization has been applied to the stack design problem. Application of this method is new in this field and different optimization strategies are tested. The results from the optimization allow to identify a clear trade-off between the compactness of the stack and the temperature level (and therefore the degradation).