  We review the calculation of spin-dependent matrix elements relevant to
scattering of weakly interacting massive particles on nuclei. A comprehensive
list, to our knowledge, of the proton and neutron total spin expectation values
($<{\bf S}_{p}>$ and $<{\bf S}_{n}>$) calculated within different nuclear
models is presented. These values allow a conclusion about the event rate
expected in direct dark matter search experiments due to spin-dependent
neutralino-nucleon interaction, provided neutralino is a dark matter particle.
