In this thesis, we focus on studying the penetration of cylinders, cones and spheres. To begin with, we have considered which curve is the result of a cross section of these three surfaces with a plane, and after that which curves we get as a result of penetration of the surfaces. We familiarize with the methods used to construct penetrating curves of two of surfaces in Monge’s projection. The first method is a cross section method with a streak of plane. Auxiliary planes could, but don’t have to, be parallel. A cross section of a surface and an auxiliary plane is a curve, whereas a cross section of another surface and the same auxiliary plane is another curve. Intersection of these two curves are points of penetrating curve. The process is repeated until there are enough points to merge them in the end. The second method is a cross section method with concentric spheres. To apply this method, two conditions have to be met: surfaces need to be rotational, and axes of surfaces have to intersect. The intersection of axes is the center of auxiliary spheres and that is the reason why we are talking about concentric spheres. If the penetration of surfaces is known and both conditions to work with the method are met, the intersections of penetrating curves one of a surface and auxiliary sphere, and penetrating curves of another surface and the same auxiliary sphere give points of looked-for penetrating curve of the surfaces. The process is repeated by choosing another sphere which shares some common points with the surfaces. In the end of the thesis, the tangent of penetrating curve is mentioned. The tangent in some point of penetrating curve is a transversal of tangential plane of surfaces in the mentioned point.