In this paper, finite element method was used for flow and strength analysis of AZ31 magnesium alloy under friction stir welding. The simulations were carried out by SYSWELD s/w, and the modeling of sheet was doned by unigraphics NX3 s/w. Welding variables for analysis were rotating speed and welding speed of tool. Also two-way factorial design method was applied to confirm the effect of welding variables on maximum temperature and stress of material used. From these results, the increaser welding speed of tool the decreaser maximum temperature, but the increaser maximum stress. Also the increaser rotating speed of tool the increaser maximum temperature, but the decreaser maximum stress. In addition the increaser welding speed of tool and the decreaser rotating speed of tool, the narrower heat effect zone. Finally rotating speed of tool influenced on maximum temperature more than welding speed of tool, and welding speed of tool influenced on maximum stress more than rotating speed of tool from the variance analysis.