Abstract: Porous carbon fiber papers, which are composed of randomly distributed carbon fibers, are now widely used in advanced structures such as fuel cells and heating materials. One of the most common working conditions for carbon fiber papers is out-plane compression. The compression deformation of carbon fiber papers has a significant impact on its mechanical, thermal and electrical properties. Therefore, understanding and revealing the out-plane constitutive relation of carbon fiber papers is essential for meeting the demand. Consequently, two nonlinear constitutive models are proposed for the porous carbon fiber papers. They are the logarithmic model considering the Hertz contact of fiber, and the power function model considering the variation of microstructure porosity and cell size. Based on the stress-strain experimental data of three commercial carbon fiber papers, the two nonlinear constitutive models proposed in the present study are compared with the traditional linear model, the mechanical properties of carbon fiber papers with/without additional organic matter are discussed. The study results indicate that: the extra resin in carbon fiber papers has an appreciable impact on the stress-strain curves, and the logarithmic-type constitutive model considering contact deformation, bending deformation and variation of structural porosity has good robustness and wide applicability; and the power-type constitutive model can accurately predict the stress-strain curves of carbon fiber papers with relatively small weight percentage resin. The determination of mechanical properties by conventional linear models for the commercial carbon fiber papers provided have relatively big errors. The comparisons indicate that the two nonlinear constitutive models proposed have good applicability in predicting the nonlinear stress-strain relation of carbon fiber papers.