In this paper we perform a model-based analysis of a solid oxide fuel cell (SOFC) system with an integrated steam reformer and with methane as a fuel. The objective of this study is to analyze the steady-state and transient characteristics of this system. For the analysis, we develop a detailed control-oriented model of the system that captures the heat and mass transfer, chemical kinetics, and electrochemical phenomena. We express the dynamics of the reformer and the fuel cell in state-space form. By applying coordinate transformations to the state-space model, we derive analytical expressions of steady-state conditions and transient behaviors of two critical performance variables, namely, fuel utilization and steam-to-carbon balance. Using these results, we solve a constrained steady-state fuel optimization problem using linear programming. Our analysis is supported by simulations. The results presented in this paper can be applied in predicting steady-state conditions and certain transient behaviors and will be useful in control development for SOFC systems.