A new crystallographic constitutive model was developed in order to capture orientation sensitive primary and secondary creep behaviors within about 20 degrees from the [0 0 1] in single crystal superalloys at the low temperature and high stress regime.  The crystal plasticity based constitutive formulations incorporate experimentally observed dislocation micro-mechanisms.  This parameterization numerically delineates the nucleation, propagation and hardening of a<1 1 2> dislocations (ribbons) that shear gamma-prime precipitates by creating stacking faults.  Detailed numerical descriptions involve slip system kinematics from a/2<1 1 0> dislocations shearing the gamma-phase matrix, a<1 1 2> stacking fault dislocation ribbons shearing the gamma-prime-phase precipitate, and interactions between the two cases.  The new constitutive model was implemented in the FEM framework, and used to predict primary and secondary creep of a single crystal superalloy CMSX-4 in three selected orientations near the [0 0 1] at 750 ^oC and 750 MPa.  Simulation results showed a reasonable agreement with the experimental data. Modeling results also indicated that a/2<1 1 0> matrix dislocations are important in limiting the propagation of a<1 1 2> SF dislocation ribbons, which leads to the transition to secondary creep.