In this paper, a random numbers model using an innovative equiperipheral grid in cylindrical coordinates has been proposed to predict the contact spot distribution of two rough surfaces at various loads. The ability of this method to predict the contact spot distribution has been proven through comparison with results using a conventional equiangular grid. Further, a network method using such an equiperipheral grid has been developed in order to solve a three-dimensional heat conduction problem where two cylindrical specimens were connected to each other along the longitudinal direction. A uniform heat flux is given at the bottom surface of specimen 1, a uniform temperature is maintained at the top surface of specimen 11, and thermal insulation is assumed at the outer radius of the two specimens. The present numerical results have been compared to calculations using conventional equiangular grids and to experimental results obtained for cylindrical brass specimens. The present results are shown to compare much more closely with experimental measurements than previous calculations using conventional numerical models. (C) 2003 Elsevier Ltd. All rights reserved.