In this paper, the matrix version of the multivariable polynomials defined by Erkus and Srivastava [Integral Transform. Spec. Funct. 17 (2006), 267-273] are introduced. With the help of these polynomials, we derive the matrix version of the Chan-Chyan-Srivastava multivariable polynomials and the multivariable extension of the familiar Lagrange-Hermite polynomials. Various families of linear, multilinear and multilateral generating functions for these multivariable matrix polynomials are presented. Miscellaneous properties are also discussed.