Tire derived aggregates (TDA) has been used successfully in numerous civil engineering projects. However, considerably few researchers investigated its performance in dynamic applications, despite the high energy absorption ability of TDA. Moreover, testing TDA samples with larger aggregate size is troublesome due to the limitation in specimen sizes available in geotechnical laboratories. Therefore, this paper provides more insights on the dynamic behavior of TDA with larger aggregate sizes. This work also investigates the extent of specimen size effect on the dynamic properties of TDA and Granulated rubber (GR). A series of undrained strain-controlled cyclic triaxial tests were performed using three specimen sizes with diameters of 70, 101 and 152 mm. TDA samples had maximum aggregate size of 19.1 and 25.4 mm, however, the GR samples had only a maximum aggregate size of 4.75 mm. All tests were performed at consolidation stress range of 25 to 100 kPa and shear strain range of 0.1 to 10%. It was found that the 70 mm specimens overestimated the shear modulus of TDA samples by a maximum of 15 to 26%. However, no significant variation was found in the shear modulus that is mobilized by the 101 and 152 mm specimens. Also, GR samples were marginally influenced by specimen size. Furthermore, regardless of the aggregate size, the damping capacity is independent of specimen size. Lastly, it is recommended to use triaxial specimen size with a diameter four times larger than the maximum aggregate size of considered TDA material.