Photomultiplier tubes (PMT) are one of the primary components of water Cherenkov neutrino detection for the Long Baseline Neutrino Experiment (LBNE). Thousands of 10- to 12-inch diameter PMT bulbs are placed in the inner wall of a detection tank or a reservoir (e.g. deep mine) filled with 10,000 gallons of high purity water with a resistivity of 11-18.24 MΩ-cm. Long-term service of PMTs is vital to the success of neutrino detection projects. This article reports the results of an investigation on the mechanical properties of PMT glasses from two vendors and the effect of ion exchange on their mechanical strength. Vickers indentation, four-point bend test, and ring-on-ring biaxial flexural strength test were used for evaluation of the mechanical strength. Chemical (potassium-sodium ion exchange) strengthening results show increased strength of 46% in one vendor glass and a 57% increase in the other, with no significant reduction in optical transmission in the ultraviolet visible range of the electromagnetic spectrum that is critical to neutrino detection. Results also show narrowing of the distribution of strength calculated using Weibull statistics with chemical strengthening for comparable exchange depths of 22-28 um.