To enhance existing theoretical frameworks previously confined to predicting surface subsidence for individual salt caverns, this study introduces an advanced model based on the stochastic medium theory. This innovative approach integrates the principle of displacement superposition and formulates equations for estimating surface settlements of twin salt caverns with varied cross-sectional geometries. Comparative analysis of numerical data reveals a high congruence between surface settlements derived from our model and those predicted by numerical results for twin salt caverns. Distinct from the conventional symmetrical 'single valley' subsidence profile associated with a solitary salt cavern, this model adeptly depicts the asymmetric 'double valley' topography characterizing twin salt caverns with diverse cross-sectional shapes. The burial depth and horizontal spacing of twin caverns significantly affect both the maximum influence radius and maximum settlement value. Conversely, the vertical spacing and dimensions of the twin caverns predominantly impact the surface settlement of each individual cavern. Critically, the inter-cavern center distance emerges as a pivotal factor in transitioning the subsidence profile from a 'double valley' to a 'single valley' configuration. This study provides scientific decision-making support for the long-term safe operation of energy storage salt caverns and the conservation of land resources.