Disturbance by ambient magnetic field is an important factor, which leads to measurement error of the laser gyro. In order to reduce the magnetic sensitivity, the polarization eigenstate in ring cavity is analyzed with matrix perturbation method, considering factors of small nonplanarity, mirror anisotropy and stress birefringence, gain and so on. The main factors affecting the magnetic sensitivity of the laser gyro are discussed. Ellipticities of eigen modes in clockwise and anti-clockwise direction caused by nonplanarity are identical and both are proportional to magnetic sensitivity. The influence of stress birefringence on ellipticity is related to mirror position, propagating direction of eigenmodes and main axis of stress. Nonplanarity is zero when ellipticities of eigen modes in clockwise and anti-clockwise direction are equal without stress birefringence in the passive cavity. A lower cavity loss is better to reduce the magnetic sensitivity of the laser gyro. The minimum magnetic sensitivity is not identical with peak gain for the laser gyro. Large phase and amplitude anisotropies of mirrors are useful to reduce magnetic sensitivity and ellipticity. These findings are significant for the reduction of magnetic sensitivity in ring laser gyros.