Formation of stray grain defects particularly around re-entrant features of the turbine blade airfoils is one of the major problems in directional and single crystal solidification processes. In this work, directional solidification tests of the GTD-111 Ni-based superalloy were conducted at different withdrawal velocities of 3, 6 and 9 mm.min^-1 using various stepped cylindrical and cubic designs. The process was also simulated using ProCAST finite element solver to characterize the crystal orientations. The phase transformation temperatures of the superalloy were estimated by the differential scanning calorimetry test. A process map was developed to predict the formation of stray grains in the platform regions of the stepped cylindrical and cubic specimens using the experimentally-validated simulation model. The process map shows critical values of the platform size, withdrawal velocity and initial sample size for the stray grain formation. The withdrawal velocity, platform size and initial sample size all had an inverse effect on the formation of stray grains.