We studied the effect of magnetoelastic anisotropy on domain wall (DW) dynamics and remagnetization process of magnetically bistable Fe-Co-rich microwires with metallic nucleus diameters (from 1.4 to 22 μm). We manipulated the magnetoelastic anisotropy applying the tensile stresses and changing the magnetostriction constant and strength of the internal stresses. Microwires of the same composition of metallic nucleus but with different geometries exhibit different magnetic field dependence of DW velocity with different slopes. Application of stresses resulted in decrease of the DW velocity, v, and DW mobility, S. Quite fast DW propagation (v until 2,500 m/s at H about 30 A/m) has been observed in low magnetostrictive magnetically bistable Co56Fe8Ni10Si10B16 microwires. Consequently, we observed certain correlation between the magnetoelastic energy and DW dynamics in microwires: decreasing the magnetoelastic energy, Kme, DW velocity increases.