The main purpose of this study is to reveal the mechanism of stratified- mixture formation in gasoline direct-injection engines. So far the authors have developed a computer code "GTT" for numerically simulating the fuel spray behavior in fuel injection engines, and have proposed the physical models for droplet breakup, spray impingement and liquid film formation on a wall, and evaporation of a droplet and liquid film, which have been applied mainly to the sprays injected from hole nozzles for diesel engines.In this study, in order to numerically simulate the hollow-cone sprays injected from a swirl injector for gasoline direct-injection engines, a physical model for hollow-cone sprays has been proposed. The injection boundary condition and the model coefficients for the droplet breakup model (improved wave breakup model) have been determined appropriately. By means of this hollow-cone spray model, the shapes and Sauter mean diameters of hollow-cone sprays in low- and high-pressure ambient gases at room temperature under the conditions for testing a swirl injector have been predicted reasonably well.Furthermore, in two types of gasoline direct-injection engines with a piston cavity of bowl-like or cup-like shape, the behavior of the fuel spray injected from a swirl injector into the cylinder in the last period of compression stroke has been numerically simulated using the GTT code. As a result, it has been shown that a cloud of fuel vapor and air mixture within combustible air- fuel ratio is formed near the spark plug at the time corresponding to ignition timing in each engine. The effect of gas flow (tumble vortex or swirl) on the stratified-mixture formation in each engine has been made clear. It is expected that the spray model and the computational results in this study can be utilized for developing gasoline direct-injection engines.