Abstract: A vacuum shield for an abrading device adapted for use upon non-uniform surfaces. The shield includes a general planar top housing mountable between a motor of the abrading device, such as a power stripper or sander, and its abrading element there. The housing includes at least an upper, a middle, and a lower surface, the middle surface including a first opening, through which a power shaft between the motor and the abrading element can pass. Each of the upper and lower surfaces are secured upon a separate downwardly-biased pivot axis to respectively opposite sides of the middle surface, for angular movement relative to an axis defined by the power shaft. The middle surface also includes a second opening for connection to a vacuum hose coupling. The shield further includes continuous flexible skirts depending from the entire length of opposite non-hinged edges of the middle segment.