This paper presents an algorithm and its implementation for computing the approximate GCD (greatest common divisor) of multivariate polynomials whose coefficients may be inexact. The method and the companion software appears to be the first practical package with such capabilities. The most significant features of the algorithm are its robustness and accuracy as demonstrated in the results of computational experiment. In addition, two variations of a squarefree factorization algorithm for multivariate polynomials are proposed as an application of the GCD algorithm.