In this work, inelastic rotational collisions of AlH with He and Ne were studied. The CCSD (T) method was used for the computation of accurate two dimensional potential energy surfaces (2-D-PESs). In the calculation of the 2-D-PESs, AlH was frozen at the experimental value of 3.1149 a(0). The recently published basis sets m-aug-cc-pV (Q+d) Z of Papajak and Truhlar, completed with bond functions placed at mid-distance between the center of mass of AlH and He/Ne atom for a better description of van der Waals interaction energy, was used throughout the computational process. The PESs of AlH-He and AlH-Ne were found to have global minima at (R = 6.9 a(0), theta = 68 degrees) and (R = 6.9 a(0), theta = 69 degrees) respectively, with corrresponding depths of 26.32 cm(-1) and 48.70 cm(-1). These potentials were fitted analytically and expanded in terms of Legendre polynomials, then used for the evaluation of the integral cross sections of state-to-state rotational transitions in AlH induced by the collisions with He or Ne within the close coupling approach. The rate coefficients are computed for low kinetic temperatures ranging from 3 K to 300 K. (C) 2014 Elsevier B.V. All rights reserved.