Abstract: Taking the flatted Gaussian beam as an example, several definitions of beam paraxiality, i.e. paraxiality estimator, degree of paraxiality, and revised degree of paraxiality, are studied analytically and illustrated numerically. It is shown that there exists a remarkable discrepancy among the three definitions when the waist width- to- wavelength ratio is small, and the paraxiality estimator will lead to a non- physical result. Whereas, the degree of paraxiality and the revised degree of paraxiality provide similar results for intermediate values of waist width- to- wavelength ratio, which are of interest in practice. Thus they both can be used for the description of beam paraxiality.