Using the Monte Carlo simulation method in the grand canonical ensemble, we Study two-dimensional symmetrical binary mixtures subjected to all external potential of square symmetry and finite corrugation. The results reveal a rich variety of mixed liquid-like and solid-like structures. It is demonstrated that even very weakly corrugated external potential leads to the development of axially ordered striped solid-like phases. The results of finite temperature simulation Confirm quite well the predictions stemming from the ground state considerations and show the formation of commensurate, high-order commensurate, and incommensurate mixed phases. It is also shown that the corrugation potential affects the demixing transition.