Thermoplastic vulcanizates (TPVs) based on high‐density polyethylene (HDPE), ethylene–propylene–diene terpolymer (EPDM), and ground tire rubber (GTR) were dynamically vulcanized with dicumyl peroxide (DCP). The polymer blend was composed of 40% HDPE, 30% EPDM, and 30% GTR, and the concentration of DCP was varied from 0.3 to 3.6 parts per hundred rubber (phr). The properties of the TPVs were determined by evaluation of the gel fraction content and the mechanical properties. In addition, IR spectroscopy and differential scanning calorimetry analysis were performed as a function of the DCP content. Decreases in the Young's modulus of the blends and the crystallinity of HDPE were observed when the content of DCP was greater than 1.8 phr. The results regarding the gel content indicate that the presence of DCP promoted the crosslinking of the thermoplastic matrix, and optimal properties were obtained with 1.5% DCP. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 39901.