The novel structure of the surge tank is often designed in hydropower stations, for example, the Coaxial Shaft Surge Tank (CSST). Reasonable mathematical modeling and physical model verification are effective methods in dealing with novel structure tanks. This study aims to analyze the influence of geometric and hydraulic parameters on the hydraulic characteristics of the Hydroelectric Generating Systems (HGS) with CSST in the transient process. First, the mathematical model of CSST and the physical model of HGS with a geometric scale of 42.33 are established. The correctness of the mathematical model is verified by the physical model test. Second, an evaluation method is proposed to optimize the specific transient parameters of HGS. The results show that the sensitivity coefficient of the diversion tunnel diameter to the highest surge in CSST is 6.09, and the impedance hole coefficient φ of CSST to the maximum water hammer pressure of the spiral casing reaches 13.47. The results also indicate that changing the diameter of the penstock can adjust the maximum water hammer pressure while keeping the surge wave in CSST unchanged. This research provides design guidance and a theoretical basis to design HGS and improve its operational safety.