Abstract Three-dimensional Monte Carlo calculations are developed for determining the energies of electron-photon showers detected in emulsion chambers. The calculations provide better accuracy and higher precision by taking into account contributions from the Landau effect, the transition effect, etc., which are hard to solve analytically. The simulation is applicable, even in the extremely high energy region (∼ 1000 TeV), for any type of chamber design, either with wide gap or alternate mixed substances. We present here two powerful ways to save computing time without sacrificing the accuracy of numerical results. The first employs approximate formulae for the cross sections of bremsstrahlung and pair creation processes, including both the screening effect and the Landau effect. The second uses analytical formula of multiple Coulomb scattering applicable when including various electromagnetic processes, such as bremsstrahlung, pair creation and ionization loss. We compared our results with FNAL data and found remarkable agreement, both for average cascades and for fluctuation. We conclude that the position of sensitive materials inserted between heavy elements critically affects the precision of the energy determination.