Axially aligned grooves can be formed on the hollow fiber membrane (HFM) inner surface under some controlled fabrication conditions during a typical immersion precipitation-based phase inversion fabrication process. Such grooved HFMs are finding promising medical applications for nerve repair and regeneration. For better nerve regeneration performance, the HFM groove geometry should be carefully controlled. Towards this goal, in this study the polyacrylonitrile (PAN) HFM groove number has been modeled based on the radially inward pressure-induced buckling mechanism. HFM has been modeled as a long six-layer fiber membrane, and the HFM inner skin layer has been treated as a thin-walled elastic cylindrical shell under the shrinkage-induced inward radial pressure. The groove number has been reasonably estimated based on the resulting buckling mode as compared with the experimental measurements.