Finite element analysis (FEA) was used to model the joining of titanium grade 2 (Ti) to AISI 321 stainless steel (SS) transition joint of lap configuration with grooves at the interface on SS side. The hot forming of Ti for filling the grooves without defects was simulated. FEA involving large plastic flow with sticking friction condition was initially validated using compression test on cylindrical specimen at 900°C. The barrelled shape and a no-deformation zone in the sample predicted by FEA matched with those of the compression experiments. For the joining process, FEA computed the distribution of strain and hydrostatic stress in Ti and the minimum ram load required for a defect-free joint. The hot forming parameters for Ti to fill the grooves without defects and any geometrical distortion of the die were found to be 0.001 s^-1 at 900°C. Using these conditions a defect-free Ti-SS joint was experimentally produced.