Tunneling under existing underground buildings has become a common issue in densely populated urban areas. The current elastic analysis for ground displacement from new tunnel construction focuses on circular tunnels. However, theoretical analysis for non-circular chamber excavations is lacking. This paper aims to develop an elastic analysis for ground deformation from non-circular chamber excavations using the ‘equivalent radius’ theory, Verruijt’s formula, and Park’s model. It adjusts the ellipticization parameter δ and uniform radial displacement ε in Verruijt’s formula. Additionally, equivalent stiffness values for diverse existing hollow structures are considered using various approaches. A comparison of the theoretical results from field measurements and simulations shows the modified equations predict ground deformation well. Finally, parametric analysis explores the impacts of non-circular cavern excavations on existing structures under different factors.