This study systematically evaluated the mechanical response of Z-type and groove-type geomembranes under a combination of normal pressure (300–1,200 Pa) and slack allowance (1 %–3 %) using a self-developed geomembrane slack-allowance tensile testing device. The experiments show that the required tension of the Z-type geomembrane is linearly positively correlated with the normal pressure, and at 1,200 Pa, with a 3 % slack allowance, the required tension is 3.62 × 10⁵ N/m, with the time-consumption curve showing nonlinear characteristics. Data integration reveals significant differences in the safety thresholds of the two methods. For geomembranes with a unidirectional Z-type slack allowance, when the slack allowance is 1 %, the maximum water head it can withstand is 71 m; when the slack allowance is 2 % and 3 %, the maximum water head is 53.5 and 51 m, respectively. For geomembranes with a unidirectional groove-type slack allowance, the maximum water heads they can withstand are 69 m when the slack allowances are 1 % and 2 % and 104 m when the slack is 3 %. The research results provide a quantitative basis for optimizing the slack allowance standards for HDPE geomembrane in hydraulic engineering.