Numerical simulations of the evolution of the vertical structure of galactic disks have been performed. The physical mechanism for the evolution is the scattering of stars off Giant Molecular Clouds (GMCs) as proposed by Spitzer and Schwarzschild (1951). A model galaxy consists of a fixed, nearly isothermal halo plus an axisymmetric, thin exponential disk consisting of 1000 stars. A population of GMCs is embedded in the disk. The stars interact with each other via a self-consistent axisymmetric field determined from an expansion in spherical harmonics to twelfth order. The stars scatter off the GMCs that are modelled as soft particles. The equations of motion of the stars and the GMCs are integrated directly to high accuracy. Adiabatic cooling is therefore included implicitly. In order to avoid axisymmetric instabilities, the stellar component is initially relatively hot in the plane of the disk. Nineteen simulations were performed with varying parameters to check the consistency of the results.