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Femtosecond laser plasma is a well-known effective source of soft and hard x-ray radiation. This x-ray radiation can be used for producing of images in medicine and materials technology, carrying out the diffraction analysis, x-ray spectroscopy with the high time resolution, studying of molecular dynamics, EXAFS spectroscopy, etc. Therefore now the problems of x-ray source efficiency increasing, spatial and time coherence degree improving, optimization of a spectrum of radiation, etc are intensively investigated. In our work we consider the possibility of usage of the elliptically tapered glass capillary for increase the x-ray radiation yield in the certain solid angle. Plasma was created by laser pulse delivered by Ti:Sa laser system (wavelength - 805 nm, pulse duration - 55 fs, pulse energy - 8 mJ) . Radiation was focused onto the surface of the melted gallium target by the lens with a focal length of 45 cm under the angle of 45 degrees. The yield of x-ray radiation was measured by photomultiplier tube FEU-119 with NaI(Tl) scintillator. In a direction of the reflected beam the part of capillary which cavity represents ellipsoid with semi-axes of 136,95 mm and 200 um was located. This capillary was used for collecting of x-ray radiation in a small solid angle. The principle of operation of a similar capillary is based on effect of the total external reflection which is observed for x-rays propagation from air to more dense optical media. Before the experiment we carried out the numerical analysis of x-rays propagation in a capillary for the purpose of estimation of the criticality of capillary input aperture position in relation to a plasma x-ray source. The analysis has shown, that for efficiency increasing more than 10 times it is necessary to locate capillary focus in area of plasma spot with accuracy better then one-two millimeters, and shift from the long axis of capillary should not be more than 50 microns. After that the technique of capillary adjustment for visible radiation reflected from the target was fulfilled. We also present the first experimental results about x-ray collection by the capillary.