The purpose of this study is to find a practical method of deriving mapping functions, which are useful in the analysis of many physical problems. The classes of regions are restricted to those which have N-axes of symmetry, which are of very important kind in practical problems. The forms of mapping functions are simple, which is advantageous in obtaining analytical solution. Application to torsional analysis and to plane-elastostatic problems have been done. Reasonable results are obtained, which show usefulness of the conformal mapping method.