Experimental investigation of sodium expansion in TiB2-carbon with different TiB2 content during aluminum electrolysis was carried out in a laboratory cell. The model based on the swelling due to the sodium penetration has been discussed, and relationship between the sodium expansion and time has been proposed that has been calculated by MATLAB. The proposed model was extended to the three-dimensional distribution of sodium concentration, stress and first principal stress that was implemented by ANSYS. Validation of this numerical tool was achieved through the Rapoport tests. The results show good agreement between analytical solution and numerical modeling as well as between experimental and numerical results. This means that the chosen numerical model is suitable to predict sodium expansion as well as induced stresses in TiB2-carbon cathodes and is great interest in the work to extend aluminum reduction cell lifetime.