Energy storage systems can effectively improve the energy efficiency and economic benefits of integrated energy system (IES) involving power-gas-heat. However, the investment and operation and maintenance (O&M) costs lack economic viability for a single park. Forming an alliance of multiple park IESs to jointly invest in shared energy storage is an effective approach to enhance both energy utilization efficiency and economic benefits, as it enables sharing flexibility and allocating O&M costs among participants. To this end, a shared energy storage planning method and a two-part cost allocation method for park IESs is proposed. In terms of planning, the shared energy storage capacity is configured to minimize the total investment and O&M costs of the multi-park IES alliance. After determining the capacity configuration, a two-part cost allocation method based on cooperative game theory is employed to reasonably allocate the investment and O&M costs of shared storage among individual park IESs. Numerical results demonstrate that the proposed planning model can rationally configure shared storage capacity, improving local renewable energy accommodation and operational economy of the multi-park IES alliance. Meanwhile, the two-part cost allocation method effectively allocates investment and O&M costs.