Various physical phenomena related to different scientific fields are governed by differential equations handled by the finite element method (FEM). The generation of the finite element mesh is necessary in order to solve a problem using the FEM. This paper deals with the renumbering of nodes and elements of the unstructured mesh created by the automatic mesh generation based on the advancing front method. The method is suitable for an efficient meshing of an arbitrary shaped domain. The mesh generator starts with a polygonal discretisation of a domain boundary representing an initial front. The generation of elements stops when the front is empty. Two renumbering algorithms related to sub-domains without touching elements and common nodes, as well as sub-domains with touching elements and common nodes, are presented in this paper. The renumbering is carried out in order to reduce the storage size required by the matrices arising in the numerical FE procedure. Thus, the node and element renumbering of the mesh generated by the advancing front method results in a lower computational effort of the FE procedure.