Abstract: Two lowest pattern dispersion and electromagnetic field of TM mode of the square coaxial line are intro duced in the article. The full wave analysis method is applied to solve the problem because it can get all results of electro magnetic after difference equation is soluted. Therefore it is very important to extent the method. The Maxwell equations of TM mode are transfer into the different equations. The Matlab code solves the different equations, then the eigenvalue and eigenvector can be gained. The Kc also can been obtained. Comparing the results of different grid dimentions and the method of solving Helmholtz equations, the same solution can be obtained. Full waves method can been adopted to solve the electro magnetics problem of TM mode coaxial transmission line.