A limited portion of a surface of a glass substrate is removed by application of a laser beam on the limited portion of the glass substrate to thereby produce a glass structure according to the invention. The glass substrate contains at least one element such as titanium, iron, vanadium, bismuth, lead, thallium, tin, cerium, rhodium or cobalt capable of absorbing energy of the laser beam and has a threshold of not larger than 1.0 J/cm2 per laser beam pulse in terms of machining energy of the laser beam. When such a glass substrate 21 is used, a glass structure having a through-hole 61 or cavity optional in sectional shape can be formed by irradiation with the laser beam 10.