In this paper some computational aspects of studying various properties of multiple orthogonal polynomials are presented. The results were obtained using the symbolic and numerical computations in Mathematica (www.wolfram.com). This paper is mainly based on papers Filipuk et al., J Phys A: Math Theor 46:205–204, 2013, [1], Van Assche et al., J Approx Theory 190:1–25, 2015, [2], Zhang and Filipuk, Symmetry Integr Geom Methods Appl 10:103, 2014, [3] (joint with W. Van Assche and L. Zhang). We also perform the Painleve analysis of certain nonlinear differential equation related to multiple Hermite polynomials and show the existence of two types of polar expansions, which might be useful to obtain relations for zeros of these polynomials.