In this report, the rigidity and strength of FRP sandwich contructions with FRP faces and light weight foam core are discussed. In the first part of this paper, basic equations of face displacements of sandwich plate with orthotropic faces under lateral load are derived by means of N. J. Hoff's theory (isotropic case). The solutions are given in the case of simply supported edges. In the second part, the results of hydrostatic pressure tests of four FRP sandwich panels are shown. Experimental results of central deflection and central strains are compared with calculations by the above theory (with shear rigidity of core as parameter), from which it was shown shear rigidity of core measured by double shear test is nonconservative. Typical examples of shear fracture of core after test are shown and considered. In the third, two kinds of bending tests (with different span and punch radius) were conducted on FRP sandwich beams cut from the above panels. It was shown typical bending fracture mode in these tests is local instability of face and core of compression side (wrinkling) and shear rigidity of core derived from these tests is excessive.