It is shown that penetration of relativistically intense laser light into an
overdense plasma, accessible by self-induced transparency, occurs over a finite
length only. The penetration length depends crucially on the overdense plasma
parameter and increases with increasing incident intensity after exceeding the
threshold for self-induced transparency. Exact analytical solutions describing
the plasma-field distributions are presented.Comment: 6 pages, 2 figures in 2 separate eps files; submitted to JETP Letter