Stable distributions have heavy tails that are asymptotically Paretian. Also they have various parameters that have made this distributions flexible. These reasons have adapted stable distributions for statistics modeling of many phenomenons. Therefore increasing attention is received in stable laws in recent years. While the problem of estimating the parameters of the univariate ?-stable law seems to have a complete solution, little is known at present about the statistical procedures for analyzing multivariate stable random samples. In this thesis we consider stable random vectors parameters and introduce their estimators, including index of stability, location and spectral measure. The major problem is estimating of spectral measure, that is a finite measure on the unit sphere of . We also simulate and compare estimators of these parameters in an empirical study.