Windows Minimum specs:
  Windows 98/ME/2000/XP/Vista
  1.2 GHz Pentium 4 (or other equivalent)
  128MB RAM
  GeForce 2 (or other equivalent)
  150MB of hard drive space

Windows Recommended specs:
  2.0 GHz Pentium 4 (or other equivalent)
  256MB RAM
  GeForce 3 or better (or other equivalent)

Mac Minimum specs:
  OS X 10.4 or 10.5
  1.5 GHz processor (PowerPC or Intel)
  128MB RAM
  GeForce 2 (or other equivalent)
  150MB of hard drive space

Mac Recommended specs:
  2.0 GHz processor (PowerPC or Intel)
  256MB RAM
  GeForce 3 or better (or other equivalent)

Mac OS X 10.3.9 should also run Depths of Peril fine, but you need OpenAL installed first.  You can download the OpenAL installer from Creative.

Depths of Peril also seems to run fine in Linux using Wine.  If you are interested in running the game on Linux, please try the demo first though.

As always system specs are very subjective.  If you are concerned about whether or not your computer can run the game as well as you would like, please download the Depths of Peril demo and find out.