DFT quantum chemical calculations have been performed in order to optimize the geometric and electronic cage structure of poly(methylaluminoxane) (MAO) with oligomerization degree n = 9–15, and to find such structures that fit most closely the existing experimental data on the MAO composition and structure. The following peculiarities of the MAO structure were found: i) In “classic” MAO (n = 9, 12, 15; Al : CH3 : O = 1 : 1 : 1), which has a triple‐layer cage structure, the inner layer contains highly reactive Al‐O bonds. ii) The reaction between “classic MAO” and trimethylaluminium (TMA) proceeds by the concerted mechanism, with the insertion of Al‐CH3 groups into these Al‐O bonds producing “true” MAO (Al : CH3 : O = 1 : 1.5 : 0.75). The calculated geometric and electronic structures of “true” MAO with n = 6, 9, 12 are presented. iii) “True” MAO and “classic” MAO exist in equilibrium. The driving force for the formation of “true” MAO is the decrease in enthalpy, and of “classic” MAO the increase in entropy, in the equilibrium reaction between “classic” MAO and TMA.