We have investigated micromachining of inorganic transparent materials by direct soft X-ray ablation. The pulsed soft X-rays were generated by irradiation of a Ta target in a vacuum chamber with Nd:YAG laser light at 532 nm, with a pulse duration of 7 ns, at a fluence of 104 J/cm2. The laser plasma soft X-rays (LPSX's) were focused on the surfaces of specimens using an ellipsoidal mirror that is made from silica glass and coated with Au. The ellipsoidal mirror is designed so that LPSX's at arount 10 nm are focused efficiently. The fluence of LPSX's on the specimens is roughly estimated to be 0.1 J/cm2. We found that quartz glass plates are machined by pulsed LPSX's irradiation at a rate of 48 nm/shot. Furthermore, the quartz plates have smooth surfaces with a roughness less thatn 10 nm after 10 shots of LPSX irradiation and sharp edges with a steepness less than 100 nm. In addition to quartz glass, the LPSX processing can be applied to micromachining of a variety of materials such as Pyrex, CaF2, LiF, LiNbO3, Si and silicone. We found a transient state induced by LPSX irradiation of quartz glass. The transient state absorbs 266 nm light. We irradiated quartz glass with 266 nm Nd:YAG laser light and LPSX's simultaneously and found that ablation is enhanced to have a rate of 85 nm/shot. With X-ray imaging optics, nanomachining of inorganic transparent materials should be achieved.