Abstract The objects with core (or with halo) are typical configuration in various astrophy-sical problems. The equilibrium and stability of the relativistic polytropes with a compact core have been discussed in this paper. Comparing with the normal polytropes, the relativistic loaded polytropes have many unique properties, some primary ones are:1. The distribution of density has a steep spike near the centre.2. The stable solution of polytropes with finite radius may exist only when the core satisfy some restricted conditions.3. When the polytropic index n≥3, the stable solution of equilibrium can also exist.