Texture evolution during friction stir welding of stainless steel was investigated using both predictions by crystal plasticity and EBSD measurements. Two- and three-dimensional Eulerian formulations are used to model friction stir welding. Plane strain deformation is assumed in a two-dimensional model, and an initial uniform texture changes into a torsion texture with monoclinic sample symmetry after deformation. Around the tool pin, the texture strengthens, weakens and restrengthens repeatedly. It is found from a simple circular streamline model that the relative magnitudes of the deformation rate and spin along the streamlines decide textural stability. In order to consider more complicated material behaviors, such as movement along the thickness direction due to a threaded tool pin and a tool shoulder, a three-dimensional Eulerian formulation is also implemented. Materials starting under the tool shoulder travel down to the bottom, producing the longest material streamlines. Those material points are predicted to have stronger texture components than others. EBSD results are compared with the predictions.