Geometric design, including the internal structure and external shape, considerably affect the thermal, fluid, and electrochemical characteristics of a polymer electrolyte membrane (PEM) fuel cell, which determine the polarization curves as well as the thermal and power inertias. Shape optimization is a natural alternative to improve the fuel cell performance and make fuel cells more attractive for power generation. This paper investigates the internal and external structure effects on the fuel cell steady and transient operation with consideration of stoichiometric ratios, pumping power, and working temperature limits. The maximal steady state net power output and the fuel cell start-up time under a step-changed current load characterize the fuel cell steady and transient performance respectively. The one-dimensional PEM fuel cell (PEMFC) thermal model introduced in a previous work [J.V.C. Vargas, J.C. Ordonez, A. Bejan, Constructal flow structure for a PEM fuel cell, Int. J. Heat Mass Transfer 47 (2004) 4177-4193] is amended to simulate the fuel cell transient start-up process. The shape optimization consists of the internal and external PEMFC structure optimization. The internal optimization focuses on the optimal allocation of fuel cell compartment thicknesses. The external optimization process seeks the PEM fuel cell optimal external aspect ratios. These two levels of optimizations pursue the optimal geometric design with quick response to the step loads and large power densities. Appropriate dimensionless groups are identified and the numerical results are presented in dimensionless charts for general engineering design. The universality of the general optimal shape found is also discussed. (c) 2006 Elsevier B.V. All rights reserved.