The Global Ionosphere-Thermosphere Model (GITM) is a nonhydrostatic model using a flexible three-dimensional spherical grid. The model solves the complete vertical momentum equation for the vertical neutral winds, and allows for nonhydrostatic solutions, which provides the capability to resolve acoustic and high-frequency gravity waves. The primary characteristics of nonhydrostatic processes and effects on the upper atmosphere are investigated using GITM. The results show that after a sudden intense enhancement of high-latitude Joule heating in a geomagnetic storm, the vertical pressure gradient force can locally be 25% larger than the gravity force, resulting in a significant disturbance away from hydrostatic equilibrium. The magnitude of the vertical wind perturbation increases with altitude and reaches 150 m/s at 300 km, which is not the typically reproduced by hydrostatic models. Nonhydrostatic processes and vertical winds are important not only in large geomagnetic storms, but also at certain locations such as cusp, SAPS, and even in equatorial region under quiet or moderate storm conditions. Meanwhile, the disturbance in the buoyancy acceleration and vertical wind caused by a geomagnetic storm propagates from the lower altitude source region to high altitudes through an acoustic wave. The nonhydrostatic processes are important to the high-frequency and small horizontal scale gravity wave propagation, and GITM simulations successfully reproduce the high-frequency gravity wave dissipation, which is consistent with the theoretical analysis. Additionally, IT response to the induced acoustic-gravity waves resulting from lower atmospheric wave forcing has been investigated using the high-resolution grids, and the simulations show clearly different wave patterns in the ionosphere and thermosphere between cases implementing the gravity wave or acoustic wave disturbances in the lower boundary.