An apparatus for regulating a leading end stacked position in a stacker for successively stacking thin sheet materials. The apparatus for regulating leading end stacked positions of thin sheet materials which are introduced into a thin sheet material stacker at high speeds, and are dropped and stacked one upon another, comprises: a retractable damping ruler normally standing by at a stand-by position upstream of a predetermined leading end stacking position, and adapted to preferentially abut the leading end of a thin sheet material each time when the thin sheet material introduced into the stacker is obliquely dropped and then retracted; a stationary ruler always located at the predetermined leading end stacking position, and adapted to finally abut the leading end of the thin sheet material, in place of the damping ruler which is retracted in association with abutting thereof against the thin sheet material; and a restoring mechanism for returning the damping ruler to the stand-by position each time when the sheet material is dropped below the damping ruler.