This work acquaints with the program Sam for interactive computer training of students on the theme "Mutual intersecting of pyramids and prisms in axonometry”. The program containing three modules – teacher, student and autopilot – allows for briefest time to teach and study the whole variety of the tasks on this theme. A classification of the pierce points of the surrounding edges of the one polyhedron with the other one, based on the mutual position of their auxiliary planes, is made. The solutions of the tasks can be traced in each of the popular axonometric projection (cabinet projection, cavalier perspective, military perspective, increased orthogonal dimetry, increased orthogonal isometry) in their significant stages as well as in each step. Each stage of the solution is accompanied by commentary. The student can manipulate any object of the drawing or can apply on the whole drawing rotation, translation, expansion, shrink, zoom, etc. The student can watch on all sides the rotating 3D image of the composition of the two intersecting polyhedrons and separate the rotating 3D image of their common part. The combination of traditional methods of training in descriptive geometry using the program Sam and the classification of the pierce points enable for a thorough, creative and self study of the students. They are instruments through which the students can not only learn in depth material for a short time, but they can prepare creative course projects such as: improvisations on a task or a selection of tasks from known sources and creating original tasks on a given topic. The program also allows to create dynamic geometric drawings.