Just about any modern PC will run elements. However if you are processing 100-200Mb Tiff files you will need a little more clout.
Here's the system requirement stated by Adobe.
# 1.6GHz or faster processor
# Microsoft® Windows® XP with Service Pack 2 or
3, Windows Vista®, or Windows 7
# 1GB of RAM
# 2GB of available hard-disk space
# Color monitor with 16-bit color video card
# 1,024x576 monitor resolution at 96dpi or less
# Microsoft DirectX 9 compatible display driver
# DVD-ROM drive