The purpose of this paper is 2-fold. It is first a continuation of the study of Massot and Rocard (1982) on the amplitude variations of the core waves near the PKP caustic, for French nuclear explosions in the South Pacific recorded on the LDG network in France. Taking advantage of a larger available data set, and using current methods to compute synthetic seismograms, such as the WKBJ method, we reinvestigate the core waves amplitude versus distance variation pattern derived by Massot and Rocard (1982). The second purpose is to give precise constraints on the PKP caustic phenomenon, using waveform and amplitude comparisons between data and synthetics. WKBJ synthetics are computed for several global spherical Earth models. Recent models with a D″ discontinuity, or a low velocity gradient at the top and the bottom of the liquid core are also tested. Our computations do not support the highly variable amplitude versus distance profile of Massot and Rocard, which displays a major peak at 145.6° and many secondary interference fringes. Between 142° and 147°, the theoretical amplitude variations we have calculated are dominated by the large PKP caustic peak, and only modulated by the simultaneous arrival of the PKIKP wave near 145°. Using a data set of 17 nuclear explosions, we have measured relative amplitudes as a function of distance, in the 142° to 147° distance range, and analyzed the waveform variations. Our observations (amplitudes and waveforms) are well modeled by the 1066B model of Gilbert and Dziewonski (1975). The agreement on amplitude variations is still good for models PREM (Dziewonski and Anderson, 1981) and IASP91 (Kennett and Engdahl, 1991). Accurate quantitative constraints are derived on the PKP caustic, among which the position of the B caustic point (144.5° ± 0.5°) for the mean 296° Mururoa-LDG network azimuth. This location depends, as a whole, on the depth of the core-mantle boundary, and on the velocity gradients in the mantle and in outermost core. Although the depth of the core-mantle boundary, and the existence of a discontinuity at the top of D″ can slightly affect the position of the B caustic point, the focusing effect at the PKP caustic is rather a global derivation of the models.