The [001] tensile and compressive flow behavior of a single crystal superalloy CMSX-4 was simulated using a "unit-cell" mesh to represent the gamma/gamma' microstructure. The simulation results showed a tension-compression (T-C) asymmetry, where the magnitude of the flow stress is larger in the elastic-plastic transition regime in tension, and is larger in compression in the plastic (flow softening) regime. The T-C flow behavior was related to the flow response of the gamma-phase matrix under the geometric and kinematic constraint of the gamma/gamma' unit cell.