Abstract: The Practical Coordinate System (PCS) has been originally defined under the condition which the value of the horizontality of the antenna pedestals is nonzero. The analytic relationship between the PCS and the Theoretical Coordinate System (TCS) is also provided strictly. Base on the above relationship and the adoption of rigorous mathematical analysis, the multivariate functional relations of the azimuth-elevation numerical readings of the target which is detected by weather radar between the PCS and the TCS were presented. Additionally, the error-analysis functions of azimuth and elevation are defined, and the analytical analysis on the problem of how the value of the horizontality of antenna pedestals of weather radar affects the target-orientation, has finally been made. The results indicate that the inaccuracy of the target-orientation caused by the horizontality of antenna pedestals of weather radar wouldn’t be greater than the value of the horizontality of antenna pedestals itself when the reading of the elevation is below 45 geometric degrees, while it increases rapidly when the value is above 45 geometric degrees. Particularly, within the vicinal space of the zenithal region, the values could exceed over hundreds of times compared with the value of the horizontality of antenna pedestals itself.