Suzaku performed observations of 3 regions in and around the Shapley supercluster: a region located between A3558 and A3556, at ~0.9 times the virial radii of both clusters, and two other regions at 1{deg}and 4{deg}away from the first pointing. The 4
{deg}-offset observation was used to evaluate the Galactic foreground emission. We did not detect significant redshifted Oxygen emission lines (O VII and O VIII) in the spectra of all three pointings, after subtracting the contribution of foreground and background emission. An upper limit for the redshifted O VIII Ka line intensity of the warm-hot intergalactic medium (WHIM) is 1.5 times 10^-7 photons s^-1 cm^-2 arcmin^-2, which corresponds to an overdensity of ~380 (Z/0.1 Z_solar)^{-1/2} (L/3 Mpc)^{-1/2}, assuming T=3times10^6 K. We found excess continuum emission in the 1{deg}-offset and on-filament regions, represented by thermal models with kT ~1 keV and ~2 keV, respectively. The redshifts of both 0 and that of the supercluster (0.048) are consistent with the observed spectra. The ~1 keV emission can be also fitted with Ne-rich Galactic (zero redshift) thin thermal emission. Radial intensity profile of 2 keV component suggests contribution from A3558 and A3556, but with significant steepening of the intensity slope in the outer region of A3558. Finally, we summarized the previous Suzaku search for the WHIM and discussed the feasibility of constraining the WHIM. An overdensity of < 400 can be detectable using O VII and O VIII emission lines in a range of 1.4times10^6 K < T < 5times10^6 K or a continuum emission in a relatively high temperature range T > 5times10^6 K with the Suzaku XIS. The non detection with Suzaku suggests that typical line-of-sight average overdensity is < 400.
