This paper presents new steady-state and dynamic models for solid oxide fuel cells (SOFCs) using core vector regression (CVR). So far, most of conventional SOFC models have been presented based on conversion laws. Due to complex mathematical equations used in these models, they are time-consuming and need large amount of memory to be applied for controller design, especially power electronic interface controller design, generation and load predictions, optimization and other studies. To overcome these problems, some black-box models, such as support vector machine (SVM) and artificial neural network (ANN)-based models have been also proposed for SOFC. In this paper, in order to model nonlinear multivariable behavior of SOFC two CVR-based black-box models are proposed for each operation mode, one for steady-state and the other one for dynamic modeling. The proposed models are trained in a very little time and need small amount of memory in comparison with existing black-box models. This is due to usage of fewer number of support vectors (SVs). In order to demonstrate the efficacy of the proposed models, they are applied to a 5-kW SOFC stack. Simulation results illustrate the effectiveness of the proposed models for both steady-state and dynamic studies. Copyright (C) 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.