To produce a precision substrate for optical and magnetic medium consisting of synthetic quartz glass and having ≤10 surface roughness (Ra), ≤0.03 μm/500μm× 500 μm surface waviness by PV value, ≤1 μm/100 mm parallel degree, and ≤2 μm/100 mm flatness degree.

This method includes a process to polish a substrate material consisting of synthetic quartz glass by using a double-face plane polishing machine equipped with an elastic deforming means. The elastic deforming means is interposed between an upper surface plate and a doughnut plate suspended from the upper surface plate and elastically deforming the substrate material by gravity. Thus, the objective precision substrate consisting of synthetic quartz glass having ≤10 surface roughness (Ra), ≤0.03 μm/500 μm ×500μm surface waviness by PV value, ≤1 μm/100 mm parallel degree and ≤2 μm/100 mm flatness degree is obtained.