This paper focuses on the problem that how to build up basic 3 bars tensegrity unit structure and how to judge its stability. Based on the outer shape geometry parameters, using node general coordinates, member vector matrices, connectivity matrices, the mathematical model of basic 3 bars tensegrity unit is presented. To build up structures automatically, a program is established in the MATLAB software by which one can build any basic 3 bars tensegrity structure under the given outer shape geometry parameters. Then, the scalar parameters force densities are introduced. With the connectivity matrices and node general coordinates, the equilibrium matrix function is built. It is linear about force densities. The balance matrix specifies the given system as one of four kinds of structures, and the stable structure can be chosen out.