Abstract We extend the Eshelby’s (equivalent) inclusion method to consider ellipsoidal volumes occupied by fluids of limited compressibility. The new method decomposes the problem into two parts – a stress free transformation problem, and a volume compatibility problem. Implemented in an open source computer code, Esh3D, the new method allows one to model interacting and fluid–solid mixed inclusions in whole and truncated spaces. We verify the new method against finite element (FE) method, showing it to be accurate and efficient.