In rigid body mechanics, confirming the principal axis of inertia of rigid body is particularly important, its calculation can be made to be simplified and favorable to study the nature and movement law of rigid body.

The principal axis of inertia of a rigid body are its symmetric axis,the rigid body is possessed of geometrical symmetry and its mass are well distributed or its mass are symmetrially distributed.

The method to calculate principal axes of inertia by adjoint matrix of eigen ma-trix is given，examples are presented.

This paper presents the eigen equation of inertial tensor expressed by the three principal invariants, which is an algebra-equation solution to calculate eigen value;proves that eigenvalue is the principal moments of inertia and that eigenvector is the principal axes of inertia;and discusses a certain method to calculate prinpal axes of inertia by adjoint matrix of eigen matrix.