A three dimensional finite element method is developed in order to analyze multidimensional phase distribution phenomena and the turbulent structure of fully developed turbulent single and two phase flows. In this paper, fully developed two phase flwo phenomena are considered without the consideration of thermal effects. three dimensional turbulent single phase flows are studied including the thermal effects. The main purpose of this study is to understand the phase distribution mechanism in single and two phase flow, i.e., to understand the hydrodynamic aspects of phase distribution phenomena, and makes it possible to predict the phase distribution numerically. Most situations of applications occur in the complex geometry so the finite element method is used to treat the geometric complexity easily. General finite element formulation for two phase flow is derived using patched finite element method. The Galerkin weighted residual method and the subregion balancing method are used for the local finite element matrix formulation. Also, penalty finite element method is introduced to remove the complexity of pressure term. The physical model is based on a two fluid model of two phase flow and the calculated results are compared with available experimental data. It can predict phase distribution, and velocity distribution including wall and core peaking phenomena in fully developed two phase flow in variety of ducts. Sensitivity studies for the several parameters are performed through numerical experiments using developed method. The developed program makes it possible to analyze phase distribution phenomena in a circula tube, which has been impossible for the state-of-the arts computer code. Temperature and velocity distribution in rod bundles can be exactly predicted in case of single phase turbulent flow using a developed program. Also applications are made for the variety of ducts such as nuclear reactor fuel rod bundles.