Critical resolved shear stresses on basal and prismatic slip systems have been estimated using an in-situ tensile test inside a scanning electron microscope coupled with a slip trace analysis. Along with the homogeneous stress field usually employed, more realistic elastic stress fields have been computed based on the FFT technique. This technique enabled to account for the elastic anisotropy of α-Ti at the grain scale as well as long range heterogeneities due to microtextured regions through the use of large dimensions EBSD maps to build 2D and 2D-extruded aggregates. Heterogeneities in the stress field are therefore observed and discussed regarding the onset of basal and prismatic slip at multiple scales. CRSS estimates are corrected accordingly.