This paper presents a mathematical model of mass and charge transport and electrochemical reaction in porous composite cathodes for application in solid oxide fuel cells. The model describes a porous composite cathode as a continuum, and characterises charge and mass transfer and electrochemical kinetics using effective parameters (i.e. conductivity, diffusivity, exchange current) related to morphology and material properties by percolation theory. The model accounts for the distribution of morphological properties (i.e. porosity, tortuosity, density of contacts among particles) along cathode thickness, as experimentally observed on scanning electron microscope images of LSM/YSZ cathodes of varying thickness. This feature allows the model to reproduce the dependence of polarisation resistance on thickness, as determined by impedance spectroscopy on LSM/YSZ cathodes of varying thickness. Polarisation resistance in these cathodes is almost constant for thin cathodes (up to 10 A mu m thickness), it sharply decreases for intermediate thickness, to reach a minimum value for about 50 A mu m thickness, then it slightly increases in thicker cathodes.