We report on studies of domain wall propagation of magnetically-bistable Fe-Co-rich microwires paying attention on the effect of applied and internal stresses. We measured magnetic domain propagation in various magnetic Fe-Co-rich amorphous microwires with metallic nucleus diameters (from 2.8 microm to 18 microm) using Sixtus Tonks-like experiments. We found that application of applied stresses and increasing of internal stresses result in decreasing of domain wall (DW) velocity. We assume that in order to achieve higher DW propagation velocity at the same magnetic field and enhanced DW mobility, special attention should be paid to the decrease of magnetoelastic energy.