Recently, much attention has been attracted to the problem of limitations on the attainable intensity of high power lasers [A. M. Fedotov et al., Phys. Rev. Lett. 105, 080402 (2010)]. The laser energy can be absorbed by electron-positron pair plasma produced from a seed by a strong laser field via the development of the electromagnetic cascades. The numerical model for a self-consistent study of electron-positron pair plasma dynamics is developed. Strong absorption of the laser energy in self-generated overdense electron-positron pair plasma is demonstrated. It is shown that the absorption becomes important for a not extremely high laser intensity I ∼ 10(24) W/cm(2) achievable in the near future.