The flux penetration near a semicircular indentation at the edge of a thin superconducting strip placed in a transverse magnetic field is investigated. The flux front distortion due to the indentation is calculated numerically by solving the Maxwell equations with a highly nonlinear $E(j)$ law. We find that the excess penetration, $Delta$, can be significantly ($sim$ 50%) larger than the indentation radius $r_0$, in contrast to a bulk supercondutor in the critical state where $Delta=r_0$. It is also shown that the flux creep tends to smoothen the flux front, i.e. reduce $Delta$. The results are in very good agreement with magneto-optical studies of flux penetration into an YBa$_2$Cu$_3$O$_x$ film having an edge defect.
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