Curved solids whose intersections have been described in this thesis are a cone, a cylinder and a sphere. Mentioned solids are solids of the 2nd order and their intersection is space curve of the 4th order. We differentiate between proper space curves and degenerated space curves and which one appears depends on the position of solids that we intersect. Proper space curves are classified as one-branch, two-branch and curves with one double point. If there comes to decomposition, a space curve of the 4th order is decomposed into curves of lower order but so that the sum of their orders equals 4. Generally, we can talk about following decompositions: four lines, two curves of the 2nd order, a curve of the 3rd order and a line, a curve of the 2nd order and two lines. Projections of curved solids and their intersection have been represented by Monge’s method and axonometry in the program for 3D modeling Rhinoceros but also with classical methods of cutting planes. In case of intersecting cylinders and/or cones, we choose cutting planes that intersect both solids along their generatrices. When one of the two solids is a sphere, we choose cutting planes that cut the other solid in the simplest possible curves. Although intersections of curved solids seem and sound complicated, their application is wide and can be found in everyday life. Here are some simple examples of their application: connecting tubes, fences, balls...Serious and creative examples are some domes and vaults.