In this paper, concrete mixes utilizing two sizes of natural aggregate and two sources of lightweight and recycled aggregates were used to investigate the effect of aggregate type and specimen size and shape on the compressive strength of concrete. In addition, samples from ready-mix concrete producers with different strengths were evaluated using standard size cylinders and cubes. Results were obtained on the 7th, 28th, and 90th day. In addition, flexural strength, split tension, and modulus of elasticity were evaluated on the 28th and 90th day. Statistical analyses were conducted to examine the significance of the difference between the compressive strength values for each two mixes using tests of hypotheses. Moreover, other mechanical properties as a function of compressive strength were discussed and compared to those predicated by the American Concrete Institute (ACI) specifications. Results indicate specimen shape has a noticeable effect on the compressive strength as the Cylinder/Cube ratio on the 90th day was ranging between 0.781 and 0.929. The concrete compressive strength and modulus of elasticity were significantly affected by the aggregate type. The flexural strength and split tensile strength were less affected by the aggregate type, which was also confirmed by the values predicted with the ACI equations.