Nowadays lattice of tetrapod-shaped elements could be used for the synthesis of constructions with high stiffness properties using new types of modern lightweight materials. The possible application of the tetrapod lattice could be constructions with unconventional design and future space structures. Previously, time consuming topology optimization approach was employed for shape optimization of such elements. It is known that metamodeling methods are efficient for shape optimization of CAD/CAE models. In this approach shape is produced by geometric boundaries defined as CAD based NURBS curves. Due to development of CAD/CAE software and advanced metamodeling techniques such approaches have become highly effective and popular in recent years. At the beginning developed technique of the shape optimization is verified on the test problem. Next in this work resource-saving technique is proposed for the shape optimization of the spatial tetrapod elements.