Modeling and visualization of the three dimensional objects are widely used in different areas of science and engineering. Fast development of computer graphics makes it possible to develop high quality images of spatial objects, and at the same time, this creates additional demands for visualization and modeling methods effectiveness. The doctoral thesis describes research results of parametrical free – form surface visualization and real object 3D geometrical modeling methods. Free – form surface visualization by ray tracing task and real objects modeling task are researched in this work. New visualization method necessity is analyzed and fortified and the developed methods effectiveness and advantages are shown. Also a comparing analysis was conducted with visualization results that were attained from existing CAD systems. In the work object modeling methods are analyzed and proposed method effectiveness and preferential on real object examples are shown, as well as practical result evaluation by expert was attained. In the frame of the doctoral theses new parametrical free – form surface visualization methods, real object 3D geometrical modeling methods and analytical 3D model volume calculation algorithm were developed. In the work, methods and algorithm theoretical basement, realization parts and experimental checkup results are shown. The practical meaning of research results and usage possibilities are shown on real objects modeling and visualization examples (computer aided design and medical engineering tasks) and experiments. The doctoral theses main results are presented at 14 international conferences, and they are reflected in 15 scientific papers. The thesis includes introduction, 4 chapters, conclusions, 6 appendices, references, 43 figures and illustrations and 10 tables, in total 180 pages. In the references list are 129 titles.