At mountain altitudes, high energy γ-ray bundles (γ-rays in parallel trajectories and with the same direction of an air shower) can be observed in the central part of air showers. These γ-ray bundles (≥ 1 TeV) and their associated air showers are observed simultaneously at Mt. Chacaltaya (5200 m) by our detectors. The γ-ray bundle in the air shower can give information on the primary composition and the characteristics of proton interaction. In this paper, we report on experimental results, simulations calculated for the present experiments, and also problems in simulations.