Cordierite has structural channels and alkaline elements can be incorporated into the channel. In order to study the incorporation effect of the alkaline and alkaline earth elements into the channel on structural and electronic properties, density functional theory calculations were performed to analyze the structural changes associated with the incorporation of alkaline and alkaline earth elements. It was found that alkaline and alkaline earth metals can be stable incorporated in the channel. Good correlation between the calculated ionic radius and the first ionization energy was observed. It was also found that the incorporated elements occupy a specific site in the channel. Incorporated elements cause the expansion of the lattice in c-axis because of the repulsive and attractive forces, interaction of the incorporated elements with the framework cations and oxygen atoms, respectively. The incorporated element at the less symmetrical sites in the channel was found to cause the more remarkable distortion.