Most direct WIMP searches have located their experimental setup under a large rock overburden in order to drastically reduce the backgrounds caused by cosmic-ray interactions. The absence of signal in current searches had led to revisit of the assumption that the WIMP-nucleon cross section is necessarily low enough to justify neglecting a possible attenuation of the WIMP flux as it passes through the atmosphere and the rock overburden. I will review recent experiments devoted to the direct search for WIMPs having cross-section large enough to escape detection in an underground site, while still being compatible with cosmological and astrophysical constraints.