We present a theoretical analysis of Gaussian beam propagation in nonlinear Kerr media by using aberration-free approximation and Huygens-Fresnel diffraction integral and obtain a simple analytic formular for Z-scan characteristics. Z-scan experiments are carried out on amorphous $As_2S_3$ thin film and compared with the theory developed, showing good agreement. The sign and the value of ${gamma}$ have been measured at 633 nm to be $+8.65{ imes}10^{-6} extrm{cm}^2/W$. We also measured the far-field intensity profiles, which confirm again self-focusing effect.