  By applying an appropriate Pekeris approximation to deal with the centrifugal
term, we present an approximate systematic solution of the two-body spinless
Salpeter (SS) equation with the Woods-Saxon interaction potential for arbitrary
-state. The analytical semi-relativistic bound-state energy eigenvalues and the
corresponding wave functions are calculated. Two special cases from our
solution are studied: the approximated Schr\"odinger-Woods-Saxon problem for
arbitrary l -state and the exact s-wave (l=0).
