The Riedel-Hiermaier-Thoma (RHT) model is extensively used in the numerical simulation and analysis of phenomena such as explosive impacts and penetration. The accuracy of the simulation results is primarily dependent on the constitutive model and the parameter values used within it. To perform sensitivity analysis and parameter determination for Lode angle correlation coefficient, the tensile yield surface parameter, the reference compressive strain rate, the reference tensile strain rate, the failure compressive strain rate and the failure tensile strain rate in the RHT model for various rock types, LS-DYNA was employed to simulate the projectile penetration into a target and split Hopkinson pressure bar (SHPB) impact tests under single-factor variations. The effects of changes in parameter values on the simulation results were analyzed, followed by an orthogonal test to assess the interaction effects between parameters and determine the optimal parameter values. The results indicate that the sensitivity ranking of the six parameters varies under different operational conditions, and the effects of these parameters on the elastic, linear strengthening, and damage-softening stages of the SHPB impact stress-strain curve were identified. Further orthogonal SHPB impact simulation tests confirm the absence of interaction between these parameters, validating that the single-factor sensitivity analysis results are effective. The optimal values for these parameters in the RHT models of granite, red sandstone, and marble are determined. This finding provides valuable insights for the sensitivity analysis and parameter determination in rock-type RHT models.