This paper uses normal mode analysis to examine topological changes in magnetic field lines at the magnetopause. For a modified Harris sheet, the normal modes include a symmetric solution (tearing mode) and an antisymmetric solution (twisting mode). Both modes form flux ropes. We studied the tearing mode in the presence of shear flow. By modeling the external region plasma with drift kinetic formalism, we found the growth rate of the tearing mode to be reduced by shear flow. On the other hand, the shear flow generates a Kelvin-Helmholtz instability which makes the magnetic field perturbation a twisting mode structure. When magnetopause parameters were used, it was difficult to induce a tearing mode in the presence of shear flow, though a shear flow twisting mode did grow under these conditions. ¿ American Geophysical Union 1992