A three-dimensional (3D) groundwater flow analysis system applying the element-free Galerkin method (EFGM) is presented. The EFGM have been applied to many problems, but a complete system that can handle 3D composite domains consisting of several materials of complex shapes, such as geological structures, has not yet been developed. Some of the challenges to be addressed are the geometry definition of analysis objects, the method of node collection for constructing shape functions, and reasonable design of the system as a whole. In our system, a unique mesh data called consistency-free mesh assembly (CMA) is introduced. A CMA is a simple assembly of meshes permitting incompatibility between adjacent meshes and overlap of meshes. The CMA is easy to generate and brings great advantages to EFGM. Some 3D numerical examples show integrating EFGM and CMA solves the problem of conventional 3D mesh generation.