  We calculate the spin independent neutralino-proton cross section for
universal SUGRA, non universal SUGRA and D-brane models with R-parity
invariance. The regions of maximum cross section in these models has started to
be probed by the current detectors. The minimum cross section generally is
>~1\times 10^{-(9-10)}pb and hence will be accessible in the future detectors,
barring special regions of parameter space where it can reduce to =~10^{-12}pb.
However, the squarks and gluinos will be heavy (>~1 TeV) in the latter case,
but still accessible at the LHC.
