The radiation hardness and mechanical strength of single- and two-phase glasses are studied for the case when nanosecond laser pulses (lambda = 1.06 mu m, tau(0.5) = 12.5 ns) are focused inside the material. Laser interferometry is applied to measure the displacement of the free surface, find optical breakage thresholds, and carry out the fractographic analysis of damaged regions. It is shown that breakdown channels and damage regions develop in a nonlinear manner according to optical breakdown mechanisms, changing each other with an increase in the laser energy. The strength of the two-phase glass is found to be more than four times that of the single-phase glass, although their elastic properties differ insignificantly. Such a considerable difference in the hardness of these materials with chemically similar constituents is attributed to the presence of the double-lattice nanometer-scale structure of the two-phase glass.