The results of studying the laser vacuum welding of the elements of heat-shielding structures made by dispersion-hardened alloys Ni–20Cr–6Al–Ti–Y$_2$O$_3$ of increased strength are presented. Also, the designs of the heat-insulating elements which are of cellular (honeycomb) structure consisting of two plates with thickness from 0.1 to 0.14 mm with fillers inside are considered. It is shown that the shallow thickness of the plates and the complexity of the design significantly complicate the possibility to firmly connect these elements and do not allow to use the known methods like diffusion welding or vacuum soldering. It is concluded that laser welding providing satisfactory structural strength and reliability can be an alternative to known methods. Local heating at certain points prevents deformation of the parts to be joined during the welding process. The use of a pulsed Nd:YAG laser with a power of 400–500 W operating in the frequency range of 50–200 Hz allows welding with and without filler metal. It has been established that the use of filler metal has practically no effect on the mechanical properties of the welded joint, however, it significantly reduces the melt zone and increases the density of the welded joint. Based on the obtained results, it is concluded that an increase of the joint strength is achieved due to the high purity of the vacuum chamber, low vacuum (less than 10$^{-2}$ Pa), and optimization of the welding process. It has been proved that the use of laser welding in vacuum when assembling elements of heat-shielding structures makes it possible to obtain a stronger and denser seam compared to known methods.