In this thesis the shape optimization technique is elaborated by using metamodels. The technique consists of designing location of the control points of polygon or knot points of NURB splines for the shape definition and building of the appropriate metamodels of responses for subsequent optimization. The smooth shapes defined by NURB splines are obtained using proposed technique. The jagged shapes are not analyzed and are excluded from the optimization process. The obtained shapes are implemented in a technologically easy way. Additionally, the design and optimization methods do not require large computational resources and can be realized by ordinary personal computer. The technique is based on using the commercial CAD software as well as the original code EDAOpt developed in RTU for design of experiments, approximation and optimization. In the 1st chapter the actuality of the thesis is discussed; shape definition techniques with NURB splines, classical shape optimization methods, recent literature of the topic are discussed. The objectives and aim of the research are stated. Actual problems and efficiency that had to be solved for proposed technique of the shape optimization are formulated. In the second chapter, the proposed technique of the shape optimization is described and verified on the base of two test problems. The first is concerned with the shape optimization of the plate bending problem with displacement constraints and the second – of the plate biaxial tension problem with equivalent stress constraints. The optimization results are compared with results of other authors. The efficiency of the three procedures of the shape definition is analyzed. It is shown that the utilization of the proposed technique and the definition of a shape by procedure of the polygon control points of NURB spline give better results than the results obtained by classical homogenization method. The results of the first test problem are validated by natural experiments. Next, the proposed technique is applied for shape optimization of real constructions elements. In each case problem is particularly considered taking into account the specific and appropriate solution that is proposed. The problems of chapters 3rd and 5th are given by Latvian enterprises Ltd “Baltic Testing Center” and Ltd “Merpro”. In the 3rd chapter the shape optimization of mounting disk for wheel pair measurements system fastening is solved. The task is developed on the basis of the wheel pair of railway freight wagon. The proposed equipment allows perform measurements for monitoring of a wagon or locomotive wheel–railing system using standard wheel pairs. The possibility to use the standard wheel pair with removable measurement equipment as tensometric wheel pair reduce the material and time expenses required for testing. Three procedures of the of the disk shape definition using only 3 design variables are considered. The optimal shape of the cross section for measurement system mounting disk is founded taking into account mechanical and technological constraints. In the 4th chapter the optimization problem of a hollow concrete block is solved. Such solutions have wide range of application for Latvian maintenance conditions. The problem consists of finding optimal shape of a hollow block considering material consumption, strength and thermo insulation. Single block is used for a thermal model which take into account heat conduction of a block materials and convection process on block external wall. Single block model with different boundary conditions and wall models with different stacking are used for strength calculations. As a result of the optimization an alternative cutout shape is obtained which can save block material. The developed shape optimization technique is applied for automobile and bus gage panel (GP) optimization in the 5th chapter. The GP must meet many requirements starting from appropriate design style and precisely measurable functional characteristics, stiffness, stress levels, weight and minimal pollution of environment. Geometrical models of GP are elaborated. Dynamic, static and also environmental impact responses, such as, carbon footprint, water eutrophication, air acidification and total energy consumed in the GP life cycle are obtained. Dynamic behaviors of the obtained alternative GP design solution are verified by analysis of the full FEM model in case of random and harmonic excitations. Next, the problems of GP brackets are solved. It is shown, that using defined restraints, the appropriate cross section shapes of solutions for bus GP brackets can be obtained. In the 6th chapter the shape optimization of the tetrapod-shaped element is performed. As was shown in the previous works, lattice of tetrapod-shaped elements have advantage properties for compressing loads. According to this, the problem of shape optimization of the tetrapod-shaped element was defined. Using developed technique the tetrapod object boundary shape effective parameterization with 3 parameters is proposed. The simplified FE model was chosen for shape optimization, which could describe behavior of tetrapod element in larger constructions. The objective maximization of tetrapod element strength with restrained volume is carried out. It is shown that obtained result could be used for new construction designs. This thesis consists of 6 chapters, conclusions and 120 references of the literature. The thesis has 13 tables and 112 figures. The thesis total size, including attachment, is 143 pages.