Evidence for nonaxial γdeformations has been widely found in collective rotational states. The γdeformation has led to very interesting characteristics of nuclear motions, such as wobbling, chiral band, and signature inversion in rotational states. There is an interesting question; why the nonaxial γdeformation is not favored in the ground states of even-even (e-e) nuclei. The quest for stable triaxial shapes in the ground states of e-e nuclei, with a maximum triaxial deformation of $ \left| \gamma \right| $ ≈ 30°, is still a major theme in nuclear structure. In the present work, we use the cranked Woods-Saxon (WS) shell model to investigate possible triaxial shapes in ground and collective rotational states. Total-Routhian-surface calculations by means of the pairing-deformation-frequency self-consistent cranked shell model are carried out for even-even germanium and selenium isotopes, in order to search for possible triaxial deformations of nuclear states. Calculations are performed in the lattice of quadrupole ( β ₂, γ) deformations with the hexadecapole β ₄variation. In fact, at each grid point of the quadrupole deformation ( β ₂, γ) lattice, the calculated energy is minimized with respect to the hexadecapole deformation β ₄. The shape phase transition from triaxial shape in ⁶⁴Ge, oblate shape in ⁶⁶Ge, again through triaxiality, to prolate deformations is found in germanium isotopes. In general, the Ge and Se isotopes have γ-soft shapes, resulting in significant dynamical triaxial effect. There is no evidence in the calculations pointing toward rigid triaxiality in ground states. The triaxiality of $ \gamma = - 30^\circ $ for the ground and collective rotational states, that is the limit of triaxial shape, is found in ^{64, 74}Ge. One should also note that the depth of the triaxial minimum increases with rotational frequency increasing in these two nuclei. The present work focuses on the possible triaxial deformation of N= Znucleus ⁶⁴Ge. Single-particle level diagrams can give a further understanding of the origin of the triaxiality. Based on the information about single-particle levels obtained with the phenomenological Woods-Saxon (WS) potential, the mechanism of triaxial deformation in N= Znucleus ⁶⁴Ge is discussed, and caused surely by a deformed γ≈30° shell gap at Z( N) = 32. At N= 34, however, an oblate shell gap appears, which results in an oblate shape in ⁶⁶Ge ( N= 34). With neutron number increasing, the effect from the N= 34 oblate gap decreases, and hence the deformations of heavier Ge isotopes change toward the triaxiality (or prolate).