Compressive strength is an essential parameter considered in making concrete. This research focus determined the compressive strength of aggregate serpentine concrete of different sizes. The obtained local Serpentine rock was crushed into four different granule sizes of 5 mm, 10 mm, 15 mm and 20 mm respectively and casting of the concrete samples, sample weight measurements and concrete sample crushing using a load testing machine for determination of the concrete compressive strength was carried out. The results of the measured density of the fabricated samples showed that the density achieved for the concrete samples with 5 mm, 10 mm, 15 mm, and 20 mm were all above the world average value of 2350 kg/m³ which revealed that the compaction of the fabricated concrete samples was optimum. The results of the corresponding compressive strengths of the concrete samples showed that the concrete with aggregate size of 10 mm met the requirement for adequate strength of an ordinary concrete which is 15 MPa followed by 15 mm aggregate size. This showed that the concrete cask design with 10 mm aggregates size from the point of view of physical strength, will withstand an external stress of magnitude up to 15 million Pascals (15 MPa) which could be attributed to the fact that better aggregate compaction was achieved at a size of 10 mm as demonstrated from the value of the density of the concrete sample. While those concrete samples fabricated with other aggregate sizes will withstand an external stress of magnitude as high as 10 million Pascals (10 MPa) in proportion to their respective compaction in the concrete matrix. Hence, from the entire results of this research work, Serpentine concrete of aggregate sizes 10-15 mm was recommended for the optimum design of a radioactive source transport cask.