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An inviscid axisymmetric model capable of predicting droplet bouncing and the detailed pre-impact motion, influenced by the ambient pressure, has been developed using boundary element method (BEM). Because most droplet impact simulations of previous studies assumed that a droplet was already in contact with the impacting substrate at the simulation start, the previous simulations could not accurately describe the effect of the gas compressed between a falling droplet and the impacting substrate. To properly account for the surrounding gas effect, an effort is made to release a droplet from a certain height. High gas pressures are computationally observed in the region between the droplet and the impact surface at instances just prior to impact. The current simulation shows that the droplet retains its spherical shape when the surface tension energy is dominant over the dissipative energy. When increasing the Weber number, the droplet surface structure is highly deformed due to the appearance of the capillary waves and, consequently, a pyramidal surface structure is formed; this phenomenon was verified with our experiment. Parametric studies using our model include the pre-impact behavior which varies as a function of the Weber number and the surrounding gas pressure.