To provide a game machine for displaying a picture in which light from a light source causes the shadow of an object, and the shadow varies according to a change in the position of the light source, the shape (posture) of the object, and so forth, while reducing a processing load. The present invention relates to a game machine for showing a picture obtained by viewing, from a predetermined viewpoint, a virtual three dimensional space where a light source and an object are placed. According to the present invention, a shadow rendering object for rendering a shadow of the object is placed. The permeability of each of the vertexes of polygons forming the shadow rendering object is determined based on the position of the light source and the position and shape data of the object, and the game screen image is produced based on the permeability determined. The number of polygons forming the shadow rendering object is controlled based on the distance between the viewpoint and the object.