In consideration of the effect of consequent elastic strain due to the lattice mismatch on the electronic structures of Quantum Dots( QDs), a six-band K·P model was used to explore the two lowest single-particle hole states in two vertically Coupled InAs/GaAs QDs (CQDs). The elastic strain due to the lattice mismatch between InAs and GaAs was included in the calculations. The theoretical results indicate that uniaxial strain effects play a dominant role in the band offset and they affect the hole states of the coupled dot system. First, it increases the splitting energy between the heavy-hole (HH) and light-hole (LH) levels and reduces the mixing of HH and LH. Simultaneously, the strain in the dot molecule affects the potential distribution of CQDs, inducing more ground states are confined on the bottom dots. Compared to the case without strain effect, the critical distance between QDs is reduced to about 2 nm, by which the hole ground states are anti-bonding-like. Therefore, the strain effects in the CQDs change the potential distribution,weaken the coupling strength between HH and LH and reduce the critical inter-dot distance.