In China's lacustrine salt rock deposits, the horizontal multi-step dissolution technique allows the construction of large-scale salt caverns within narrow salt layers. However, insoluble thin interlayers in the strata, which are unavoidable, substantially influence the expansion patterns of horizontal cavities. Additionally, ground stress conditions during operation influence the stability of gas storage reservoirs constructed at depth. To address these challenges, a physical simulation device was designed to replicate the expansion and reshaping of horizontal cavities, mirroring the horizontal multi-step dissolution technique in salt rock containing narrow interlayers. By modifying the positional parameters of the interlayers, a series of salt cavern models with varying shapes and capacities were produced. Reverse engineering techniques were employed to reconstruct threedimensional geological models of the horizontal salt caverns based on experimental results. These models were subsequently employed to evaluate the stability and utilization of the surrounding rock under high ground stress conditions. Results show that narrow interlayers alter saline flow paths, resulting in a flat-topped structure at the cavity apex. When the interlayer approaches the horizontal well, cavity volume and height decrease, while the breadth of the cavity top increases. This effect intensifies as the interlayer nears the injection well. Under a ground stress regime dominated by horizontal stress, the study further reveals that as the side pressure coefficient increases, indicators such as cavity volume shrinkage rate, plastic zone volume in the surrounding rock, vertical displacement, and equivalent strain all exhibit an upward trend, while the safety factor declines, resulting in decreased stability. Notably, when the side pressure coefficient exceeds 1.5, the impact of ground stress on the stability of the salt cavern gas storage becomes significantly more pronounced. These findings provide critical theoretical insights and practical guidance for designing horizontal cavity construction in deep salt layers and developing geological energy storage systems.