The safe and stable function of hyper-compressors with operating pressures exceeding 180 MPa is a guarantee for the low-density polyethylene production process, and the transient dynamics of the compressor shaft system under stable operating conditions are an important concern for the design, maintenance, and fault detection of such compressors. Therefore, this paper presents a finite-element model of the hyper-compressor shaft system and analyzes the dynamic stress and fatigue life of the crankshaft, the connecting rod, the crosshead, and the plunger. In order to verify the accuracy of the model, all stages of the compressor's plunger stress and the torque of the crankshaft–motor connection end were tested in the field. The dynamic gas pressure of each stage cylinder was obtained by the tested stress of the corresponding plunger, then it was set as the load input of the finite-element model. The results show that: the average errors of the simulated plunger stress at two stages are 0.14% and 0.21%, respectively; the mean, peak, valley, and range errors of the torque at the crankshaft–motor connection end are 3.80%, 12.37%, and 3.49%, respectively; the simulated first-order torsional natural frequency of the shaft system is 78 Hz with an error of 8.3%. In the occurrence of the first-order torsional resonance, the maximum torsional stress appears at the crankshaft–motor connection end. The maximum dynamic stress alternating amplitude of the hyper-compressor shaft system under stable operating conditions is 103.7 MPa with a minimum life of 3.309 × 109, which occurs at the crankshaft–motor connection end and is converted into 31.48 years. The finite-element model, test, and simulation data presented in this paper can provide a reference for the fault detection and optimization design of hyper-compressors.