A significant number of subsalt oil and gas fields are distributed worldwide. Due to the high costs associated with coring operations in salt formations, conducting creep experiments on specific salt rock cores is challenging. To address this issue, a method for creating artificial salt rock cores was developed wherein the degree of recrystallization was controlled by adjusting the preparation temperature and pressure. By testing the acoustic velocity, density, and uniaxial peak strength of salt rock cores under different preparation conditions, the optimal preparation conditions were identified. Creep experiments verified that the artificial salt rock cores exhibit similar creep characteristics to natural salt rock cores, indicating the feasibility of using artificial cores as substitutes for natural ones. Based on indoor creep experiments, a viscoelastic constitutive model of salt rock was constructed. The result showed that the rheological characteristics of the decelerating creep stage conform to the Kelvin model, while the steady-state creep stage aligns with the Heard model. A UMAT subroutine was compiled to describe the creep characteristics of the decelerating and steady-state stages, demonstrating a good fit and indicating the applicability of the viscoelastic model constructed in this study. Creep experiments on composite salt rocks with different contents of anhydrite showed that the presence of anhydrite inhibits the creep of salt rock. The higher the anhydrite content in the salt rock, the lower the creep rate of the rock. Therefore, in salt layers containing anhydrite, the density of drilling fluid used during drilling can be appropriately reduced.