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Electrical contact resistance (ECR) at the interface is of significant importance in many fields of science and engineering. Current methods for contact resistance estimation are based on the typical nearly incompressible rough surfaces, which is not suitable for porous material with large deformation in the compression process. The objective of this work is to build an analytical model for ECR between solid material and porous material, for example, which could be used to predict power loss between carbon fiber paper and bipolar plate in the fuel cell. First, mathematical description of solid roughness surface is built by classic Greenwood and Williamson model. Considering the porous structure, carbon fiber paper is modeled by multi-layer construction based on random line network model. Effect of large compression of carbon paper on contact behavior is furtherly given necessary attention in this study. Contact pressure and resistance are calculated based on statistical methods with consideration of multi-deformation states. Then, experiments are carried out to validate the numerical model. The results show good agreements with the numerical model. Finally, influences of carbon paper compression and main parameters are systematically discussed based on the numerical model. The model developed will enhance our understanding regarding the relation between contact pressure and contact resistance at the interface for solid material and fiber-structure material. [ABSTRACT FROM AUTHOR]