During the operation of drilling rigs, bolts are subjected to significant loads, rendering bolt groups vulnerable to failure due to uneven load distribution. This study investigates the multi-bolt load distribution characteristics of eight-gear and four-gear symmetric transmission mechanisms in drilling rigs. The spring stiffness method is utilized to analyze multi-bolt load distribution. A finite element model of the bolted connection is developed by integrating the structural shape and transmission mechanism. The model’s accuracy is validated through a rack strain test under various loads. Based on the finite element analysis results, this study proposes an evaluation method for bolted connections using relative deformation difference. The impacts of bolt pitch, end distance, preload, and thickness of the derrick connection plate under different load positions on the connection are examined. This paper presents a methodology and conclusions that can inform the design of bolted connections for heavy-duty drive systems.