Quasi-static and high cycle fatigue tests have been conducted on brick masonry test specimens under laboratory dry, wet and submerged test conditions. The relatively low compressive strengths of the bricks and mortar used to manufacture the test specimens were intended to be representative of the type of bricks and mortar likely to be encountered in relatively old masonry arch bridges. The quasi-static test results indicate that the compressive strength of brick masonry increases with an increase in the compressive strength of the mortar, and decreases with an increase in the degree of saturation. The compressive strength of brick masonry, based on assumed linear no tension stress distributions, increases with an increase in the load eccentricity or stress gradient. Approximately 20% of the apparent increase in compressive strength due to load eccentricity can be attributed to non-linear material behaviour, resulting in non-linear no tension stress distributions in the mortar joints. The high cycle fatigue tests on laboratory dry, wet and submerged test specimens indicate that the fatigue strength of brick masonry depends upon the induced stress range, the mean or maximum induced stress and the quasi-static compressive strength of the brick masonry under similar loading conditions. A lower bound fatigue strength curve for laboratory dry, wet and submerged brick masonry is proposed.