The characteristic features of electromagnetic cascade showers initiated by high-energy γ-rays are examined in detail with the Monte Carlo method under the approximation A. The treatment is made three-dimensionally, in which an device is introduced for taking into account the deviations of shower particles from the shower axes. The various kinds of quantities, some of which can not, in principle, be derived with the analytical method, are computed and some of them are compared with those derived by the latter method. From the comparison of the Nishimura-Kamata function with our empirical lateral distribution function of electrons which is derived by the least square fitting to the computed data, it is shown that the Nishimura-Kamata function evaluated for infinite primary energy may not be applicable unconditionally. Some other distribution functions are also given. Special attentions are devoted to the fluctuation problem of various quantities. Their variances and their coefficients of variation are presented and discussions on their interrelations are given. These results mentioned are fully used to get a useful clue to the estimation of the energies of primary γ-rays and their production heights. Some basic arguments on this problem are given, which will be useful for applications.