In order to improve the long-term reliability and durability of solid oxide fuel cells (SOFCs), high-resolution models that capture the most important phenomena are urgently required. In this study, a fully coupled electro-chemo-thermo-mechanical model is developed and applied for a planar SOFC aiming to determine the distribution of the current density, the mole fraction distribution of the gas species, the temperature field and the mechanical stresses. Effective material properties of an anode have been obtained by the finite element homogenisation of a representative volume element of porous multicomponent anode microstructure and are incorporated into the model. The study aims primarily to describe the creep of electrodes. The power-law-type Norton creep model with Hill equivalent stress is used for the modelling of anisotropic creep of SOFCs. A method for identifying the parameters of the orthotropic creep model for porous metal/ceramic anode is proposed, which is applied for the homogenisation of a real microstructure of Ni8YSZ and used for SOFC creep process simulations. Multivariant three-dimensional numerical simulations of SOFCs with co-flow and counter-flow configurations are performed, which reveal, for instance, the different relaxation rates of the SOFC components due to the creep behaviour.