Summary: FETI-DP (dual-primal finite element tearing and interconnecting) methods are nonoverlapping domain decomposition methods which are used to solve large algebraic systems of equations that arise, e.g., from problems in linear elasticity. Good convergence bounds for problems of compressible linear elasticity are well known for two- and three-dimensional problems. More recently, FETI-DP and BDDC (balancing domain decomposition by constraints) methods have been developed that are robust also in the regime of homogeneous almost incompressible linear elasticity. The coarse space of such methods is large especially in 3D (three dimensions) and its implementation needs knowledge of geometrical information. Here, the convergence of FETI-DP methods for problems in 3D with almost incompressible inclusions or compressible inclusions with different material parameters embedded in a compressible matrix material is analyzed. For such problems, where the material is compressible in the vicinity of the subdomain interface, a polylogarithmic condition number estimate is shown for the preconditioned FETI-DP system. This bound depends only on the thickness of the compressible hull but is otherwise independent of coefficient jumps between subdomains and also between the hull and the inclusion. The bound is also valid for corresponding BDDC methods. The new contribution of the current paper is a theory that provides condition number bounds for the case of varying incompressibility and also varying Young moduli inside subdomains without changing the coarse space.