The rubber cylinder is the core sealing element of a compression packer, and its structural stability directly determines downhole sealing reliability. The rubber cylinder is made of HNBR, while the central tube, support rings, and casing are made of 35 CrMo steel. During axial compression, the rubber cylinder may undergo localized creasing instability characterized by sharp self-contacting folds, inducing severe stress concentration and degrading sealing performance. This paper presents a systematic finite element investigation of creasing behavior in rubber cylinders, focusing on meshing strategy, interfacial friction, and geometric parameters. A refined meshing strategy is proposed that captures creasing and self-contact, demonstrating that a mesh size less than 0.5 mm is required. A zone-specific friction model distinguishes the tribological roles of different interfaces: increasing friction at the support ring suppresses shoulder protrusion, while increasing friction at the central tube reduces contact stress. For the packer geometries and operating conditions investigated, the critical expansion ratio at which the crease initiates is approximately 1.13. Increasing rubber cylinder length and reducing radial clearance are identified as effective measures to suppress creasing. The logarithmic strain at crease nucleation is approximately −0.66, which is more negative than the Biot linear bifurcation threshold (−0.61). This deeper strain is mechanically attributed to bulging-induced curvature and superimposed bending compression, confirming the crease as a nonlinear instability. This work provides numerical references for the anti-creasing design of packer rubber cylinders under quasi-static setting.