Self-assembled quantum dots (DQ) can be grown as stacks where the QD distance can be controlled with atomic layer control. This distance determines the interaction of the artificial atom states to form artificial molecules. The design of QD stacks becomes complicated since the structures are subject to inhomogeneous, long-range strain and growth imperfections such as non-identical dots and inter-diffused interfaces. This study presents simulations of stacks consistent of three QDs in their resulting inhomogeneous strain field. The simulations are performed with NEMO 3-D which uses the valence force field method to compute the strain and the empirical sp3ds * tight binding method to compute the electronic structure. Strain is shown to provide a very interesting mixing between states and preferred ordering of the ground state in the top-most or bottom most quantum dot subject to growth asymmetries.