Solid oxide fuel cells (SOFCs) are very promising for their potential applications as power generators. However, the cost of these cells needs to be significantly reduced to make them a commercial success. Cost of the materials is a significant component of the overall cost. An improvement of the power density with respect to the weight of the cell, termed as gravimetric power density in this study, can help to achieve a lower material cost. On the other hand, a compact design is required for both man-portable and stationary powerhouse applications. The power density with respect to the overall volume of the cell is termed as volumetric power density in this study. A nonlinear constrained multiobjective optimization study using a lexicographic approach is performed to maximize the gravimetric and the volumetric power density of a tubular SOFC. The decision variables are the radius of the anode channel, the cell length, and the annulus size. To be used for optimization studies, a detailed steady state model is developed that can capture changes in the concentration, activation, and ohmic losses due to changes in the decision variables. The model is extensively validated with experimental data collected from an industrial cell spanning a wide range of temperatures, H2 flow rates, and DC polarizations. Although the model predictions are found to be satisfactory for most operating conditions, a significant mismatch between the simulation results and the experimental data is observed when the H2 flow rate is low. The validation study helps to identify the feasible region for the optimization study. The optimization study shows that significant improvements in both the power densities are possible for all the operating conditions considered in this study. The electrical efficiency of the cell also gets improved due to the optimization. In one of the operating conditions, about 30% improvement in the gravimetric power density and about 65% improvement in the volumetric power density are obtained due to the optimization. The percentage changes of the decision variables compared to their base case values are found to be similar for all the voltages other than the voltages close to the open circuit potential (OCP). © 2010 Elsevier Ltd.