Polydimethylsiloxane (PDMS) is a material used for cell culture substrates / bio-chips and micro total analysis systems / lab-on-chips due to its flexibility, chemical / thermo-dynamic stability, bio-compatibility, transparency and moldability. For further development, it is inevitable to develop a technique to fabricate precise three dimensional structures on micrometer-scale at high aspect ratio. In the previous works, we reported a technique for high-quality micromachining of PDMS without chemical modification, by means of photo direct machining using laser plasma EUV sources. In the present work, we have investigated fabrication of through holes. The EUV radiations around 10 nm were generated by irradiation of Ta targets with Nd:YAG laser light (10 ns, 500 mJ/pulse). The generated EUV radiations were focused using an ellipsoidal mirror. It has a narrower incident angle than those in the previous works in order to form a EUV beam with higher directivity, so that higher aspect structures can be fabricated. The focused EUV beam was incident on PDMS sheets with a thickness of 15 micrometers, through holes in a contact mask placed on top of them. Using a contact mask with holes with a diameter of three micrometers, complete through holes with a diameter of two micrometers are fabricated in the PDMS sheet. Using a contact mask with two micrometer holes, however, ablation holes almost reaches to the back side of the PDMS sheet. The fabricated structures can be explained in terms of geometrical optics. Thus, we have developed a technique for micromachining of PDMS sheets at high aspect ratios.