We made a computational study of electron wavefunction symmetry in two types of InAs/GaAs self-assembled quantum dot (QD): one is a normal domical and pyramidal Stranski-Krastanow(SK)-type QD but embedded in InGaAs strain-reducing layer, and the other is a columnar-shaped QD fabricated via direct perpendicular stacking of SK-type QDs. Our calculations based on the three-dimensional finite element method suggested that the in-plane symmetry of the electron wavefunction is superior to that of the crystallographic QD structure. The presence of an InGaAs strain-reducing layer helps to improve the symmetry of SK-type QD. The higher the indium composition of the strain-reducing layer, the greater the improvement. The improvement is greater with domical QD than with pyramidal QD. We also found that the multiple wetting layers around the columnar-shaped QD structure act as a strain-reducing layer, so that the improvement of symmetry is dependent on the average indium composition of the multiple wetting/interval layers. The symmetry improvement was explained by the wavefunction overflow outside the QDs. We found that, to achieve highly symmetric wavefunction, the strain-reducing-layer-embedded QDs are adequate more than the columnar-shaped QDs. These results will aid in the development of an entangled-photon generator that requires symmetric in-plane QD structure.