The proposed approach consists in extending an existing sequential mesh generator in order to design a parallel mesh generator. A sequential three-dimensional mesh generator builds the internal mesh by applying advancing front techniques from a surface mesh defining the volume of the initial domain. We geometrically decompose the domain by recursively splitting it into subdomains using cutting planes. We run a sequential mesh generator code on different processors, each of them working on a single subdomain. The interface mesh compatibility on the two sides of two subdomains makes it possible to merge the results. We present in this paper our modular approach, an example of a interface mesh generation, and we specify the cutting plane decomposition method.