The analytical solution for the problem of transient thermal conduction with solid body movement is developed for an orthotropic parallelepiped. Transformations are used to eliminate the flow terms and the orthotropic dependence. The solution uses two types of Green's functions: one coming from the Laplace transform method and the other from the method of separation of variables. The solution method is powerful because it incorporates internal verification of the numerical results by varying the partition time between the short and long components. An example is given for a multi-dimensional case involving both prescribed heat flux and temperature boundary conditions. (C) 2004 Elsevier Ltd. All rights reserved.