A challenge in the further development of lithium ion batteries is the reduction of the measurable capacity fade. One mechanism leading to electrode degradation is particle cracking due to the intercalation of lithium into the host material. This leads to considerable volumetric strain, and therefore, to mechanical stresses which can exceed the particle strength. In order to estimate the magnitude of the arising intercalation-induced stresses, a numerical model was developed for a single particle consisting of LiCoO2. Special consideration was paid to the influence of phase segregation on mechanical stresses. A three dimensional model was developed in order to cover the influence of anisotropic particles with spheroids used as model system.