The precision technique for side polishing of single-mode quartz fibers is developed. The technique comprises cutting curved groove in silica block, gluing a section of bare fiber into the groove, and subsequent grinding and polishing of the silica block/fiber assembly. We succeeded in fabricating up to six side-polished fibers in one block with effective interaction length 2-4 mm. The accuracy of polishing depth was achieved at 1 micrometers using in-situ monitoring of transmission of 1.3 micrometers laser light through the fiber. The developed technique combines high accuracy, reproducibility and low cost in commercial production. Side- polished single-mode fibers fabricated with this technique can find application as elements of Bragg grating transmission filters, narrowband reflectors, optical add/drop multiplexers, couplers, polarizers, sensors, etc.