A linear to radial and/or azimuthal polarization converter (LRAC) has been inserted into the beam delivery of a micromachining station equipped with a picosecond laser system. Percussion drilling and helical drilling in steel have been performed using radially as well as azimuthally polarized infrared radiation at 1030 nm. The presented machining results are discussed on the basis of numerical simulations of the polarization-dependent beam propagation inside the fabricated capillaries.