We define the Exton’s triple hypergeometric function X2 of matrix arguments and establish some integral representations for this function which generalize the corresponding results of Choi, Hasanov and Turaev (Choi, Junesang, Hasanov, Anvar and Turaev, Mamasali, Certain integral representations of Euler type for the Exton function X2, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 17(4), (2010), 347–354) for the matrix arguments case.