  The differential cross-section for the elastic scattering of the lightest
supersymmetric particle (LSP) with nuclear targets is calculated in the context
of currently fashionable supersymmetric theories (SUSY). An effective four
fermion interaction is constructed by considering i) $Z^0$ exchange ii)s-quark
exchange and iii) Higgs exchange. It is expressed in terms of the form factors
$f^0_V,f^0_A, f^0_S$ (isoscalar) and $f^1_V,f^1_A$ and $f^1_S$ (isovector)
which contain all the information of the underlining theory. Numerical values
were obtained using representative input parameters in the constrained
parameter space of SUSY phenomenology. Both the coherent and for odd-A nuclei
the incoherent (spin) nuclear matrix elements were evaluated for nuclei of
experimental interest. The spin matrix elements tend to dominate for
  odd nuclei but the coherent matrix elements become more important in all
other cases. For the coherent part the Higgs contribution competes with the Z-
and s-quark contributions. Cross-sections as high as $10^{-37} cm^2$ have been
obtained.
