This article deals with the implementation of the lattice Boltzmann method (LBM) for the analyses of non-Fourier heat conduction in 1-D cylindrical and spherical geometries. Evolution of the wave like temperature distributions in the medium is obtained, and analysed for the effects of different sets of thermal perturbations at the inner and the outer boundaries of the geometry. The LBM results are validated against those available in the literature, and those obtained by solving the same problems using the finite volume method (FVM). Results of the LBM are in excellent agreement with those reported in the literature, and with the results from the FVM. Computationally, the LBM has an advantage over the FVM. (C) 2012 Elsevier Ltd. All rights reserved.