To prevent a cutting fault due to deviations in breaked positions at the time of cutting a glass substrate.

This glass substrate cutting device is made to be a structure in which a porous elastic body 2 for sucking a glass substrate 3 is stretched on a surface plate 1 and peripheral parts of the porous electric body are fixed to porous elastic body extending guides 5 and the peripheral parts of the elastic body can be extended by a porous elastic body extending mechanism 6. The arrangement of sucking hole 7 is made so that the density of the holes in the peripheral parts is made larger than that in the central part and the peripheral parts are made so as to surely suck the glass substrate 3. Cutting property is enhanced by generating tensile stresses on surfaces of the glass substrate of sucked sides while extending the porous elastic body 2 a little in this state.