This paper aims to evaluate the influence of concrete blocks and grout’s properties on the masonry’s compressive strength and stiffness. Prisms were produced with blocks and grouts with different strength levels, and mortars with strength of 70% of the blocks’ net area strength. It was possible to understand the effects of using low strength and high strength blocks, check the effectiveness of using grout or increasing its strength, and develop response surfaces, contour graphs, and empirical equations. Predictions about the masonry failure mechanisms are proposed for different block and grout combinations. It helps the designer to associate strength and failure mechanisms, prevent or mitigate their undesirable consequences, and eliminate brittle rupture modes. Results complement the existing database and can be used to properly select blocks and grout for masonry structures.