High Altitude Platform Stations (HAPSs) revolutionize telecommunications by delivering wide-area coverage and enhanced connectivity from the stratosphere. However, seamless communication relies on efficient handoff mechanisms, which are crucial for minimizing latency and ensuring uninterrupted connectivity as users transition across coverage zones. The proposed study explores the handoff process in HAPS and offers a more comprehensive analytical framework. While Markov models have been extensively utilized for analyzing handoff processes in satellite systems, this research proposes a Semi-Markov Model (SMM) to provide a more realistic evaluation. This SMM incorporates distinct phases of the handoff process—initiation, preparation, execution, and completion—enabling a detailed assessment of the system performance under non-exponential state holding times. Closed-form expressions are derived for performance measures including steady-state probabilities, expected number of packets, transmission delay, expected number of packets in the queue, and mean waiting time. Numerical results demonstrate that the initiation state service rate has the most significant impact on system performance, while variation in service rate in preparation, execution, and completion states exhibit an insensitivity effect when the combined service rate is fixed. In addition, a comparative analysis against the classical M/M/1/N queuing system demonstrates that the proposed SMM provides a realistic representation of the handoff process, thereby enabling a more accurate evaluation of system performance measures.