A substrate for an information recording medium, which substrate is made of a highly heat-resistant and low-alkali-elution glass and is suitable as a substrate for forming a perpendicular-magnetic-recording-mode layers thereon at a high temperature with a sputtering machine, the substrate being made of an alkali-metal-oxide-containing glass having a glass transition temperature (Tg) of 620.degree. C. or higher and satisfying a requirement that the alkali ion elution amount per a unit area when the glass is immersed in water having a temperature of 80.degree. C. for 24 hours is 0.2 .mu.mol/cm.sup.2 or less, an information recording medium having an information recording layer formed on the substrate, and a process for producing the information recording medium.