The objective of this paper is to present the element connectivity parameterization (ECP) fur three dimensional problems. In the ECP method, a continuum structure is viewed as discretized finite elements connected by zero-length elastic links whose stiffness values control the degree of inter-element connectivity. The ECP method can effectively avoid the formation of the low-density unstable elements. These elements appear when the standard element density method is used for geometrical nonlinear problems. In this paper, this ECP method developed fur two-dimensional problems is expanded to the design of three-dimensional geometrical nonlinear structures. Among others, the automatic procedure converting standard finite element models to the models suitable for the ECP approach is developed and applied for optimization problems defined on general three-dimensional design domains.