Abstract Research purposes: With the development of high － speed railway，the catenary should be assembled with more precision and the mechanics of the catenary should be calculated more precisely． However，the most of the current mechanics models for the catenary are the 2D ones and they can not reflect the actual situation of the catenary exactly． So the calculation of the real mechanics of the catenary can be realized by establishing the 3D model． Research conclusions: In this paper，the research is done on the 3D model for the catenary and the systematically static balance equation is offered． The non － linear equations are obtained with iteration method to solve the problem of static balances under the different loads． Also the change of the balance positions of the catenary under the different conditions is researched through calculation of the suspension chord length． These three kinds of the 3D model are available for researching the dynamic effect of the pantograph and catenary and with them，the vivid simulation models can be obtained． The model accuracy is tested and verified by calculating the wind yaw with the 3D model for three － span catenary．
Li Ruiping． Finite Element Model for Catenary in Initial Equilibrium State ［J］． Journal of Southwest Jiaotong University，2009( 5) : 732 － 737．
［6］ Benet，J． ，Alberto，A． ，Arias，E． ＆ Rojo，T． ，A Mathematical Model of the Pantograph － Catenary Dynamic Interaction with Several Contact Wires［J］． IAENG International Journal of Applied Mathematics， 2007( 2) :136-144.
2011, Vol. 28 
