We present an analysis of a mosaic of ROSAT PSPC and Einstein Observatory IPC X-ray observations of 14 clusters and two groups of galaxies, enclosed in a sky area of 15 degrees x 20 degrees centred on A3558 within the Shapley Supercluster region. From the mass of each cluster, extrapolated to a density contrast of 500, we define four large structures: (1) the core of the Shapley Supercluster with radius 13 h(50)(-1) Mpc; (2) the core plus A1736; (3) the core, A1736 and the western extension (A3528-A3530-A3532) and A3571; and (4), adding the northern cluster pair A1631-A1644 to structure (3), the supercluster as a whole enclosed within a radius of similar to 90 h(50)(-1) Mpc. The observed total masses range between 3.5 and 9.5 x 10(15) M-.. The mass values derived from the observed intracluster gas (assuming a baryon fraction consistent with primordial nucleosynthesis) are of the order of a few times 10(16) M-.. Given these estimates, the core is a bound structure with a very significant overdensity of at least 5 times the critical density, indicating that it is approaching maximum expansion before collapsing. Structure (2) has an overdensity of 1.7 on a scale of similar to 30 h(50)(-1) Mpc. The core is then a 2 sigma - 3.7 sigma fluctuation in an initial Gaussian perturbation field, normalized for galaxies and clusters. The highest value applies if we extrapolate to a density contrast of 200 and assume that Omega(b) < 0.095. The baryon fraction of the core of the Shapley Supercluster, with A1736, is about 15 per cent over a radius of 28 h(50)(-1) Mpc.