In order to estimate longitude and latitude shafts rigidity and resolve conflict between shaft error test result and actual work performance of the 40 cm alt-alt telescope, vibration modes and gravity deformations at the different angles of the shaft were analyzed respectively by Finite Element Method (FEM). Frequencies and the max deformations of longitude and latitude shafts indicated that shaft rigidity satisfied the design requirement. From 0° to 180° longitude angle, longitude shaft shake error caused by gravity deformation was calculated. The shake error caused by structure deformation has the same sinusoidal variation pattern with the shaft error test result. The longitude shaft precision amendment is obtained by the compensation method that subtracting the calculated results from the test result. The shaft precision PV value is improved from 7.2″ to 2.6″ and the RMS value is improved from 0.7″ to 0.3″. The corrected shaft shake error is consistent with actual work performance state, and represents actual performance of the alt-alt telescope longitude shaft.