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Silicon and strontium are key elements to explore the nucleosynthesis and chemical evolution of the Galaxy by measurements of very metal-poor stars. There are, however, only a few useful spectral lines of these elements in the optical range that are measurable for such low-metallicity stars. Here we report on abundances of these two elements determined from near-infrared high-resolution spectra obtained with the Subaru Telescope Infrared Doppler instrument. Si abundances are determined for as many as 26 Si lines for six very and extremely metal-poor stars (−4.0 < [Fe/H] < −1.5), which significantly improves the reliability of the abundance measurements. All six stars, including three carbon-enhanced objects, show over-abundances of Si ([Si/Fe] ∼ +0.5). Two stars with [Fe/H] ∼ −1.5 have relatively small over-abundances. The [Mg/Si] ratios agree with the solar value, except for one metal-poor star with carbon excess. Strontium abundances are determined from the triplet lines for four stars, including two for the first time. The consistency of the Sr abundances determined from near-infrared and optical spectra require further examination from additional observations.