Summary: The analytical solutions of unsteady heat conduction with variable thermal properties (thermal conductivity, density and specific heat are functions of temperature or coordinates) are meaningful in theory. In addition, they are very useful to the computational heat conduction to check the numerical solutions and to develop numerical schemes, grid generation methods and so forth. Such solutions in rectangular coordinates have been derived by the authors. Some other solutions for 1-D and 2-D axisymmetrical heat conduction in cylindrical coordinates are given in this paper to promote the heat conduction theory and to develop the relative computational heat conduction.