We investigate the phase behaviour of a single-component system in three dimensions (3D). The particles are interacting via a core-softened shoulder potential. Using standard N, V, T Monte Carlo and Gibbs-ensemble simulations, we obtain the complete gas-liquid phase behaviour, the coexistence line and the gas-liquid critical point in 3D for this potential for the first time. We develop an equation of state by means of a modified Benedict Webb Rubin (MBWR) equation. We then focus on thermodynamic anomalies of the liquid phase. We show for the range we have studied that anomalies like the maxima in the density and compressibility as a function of temperature known in the 1D and 2D case of that potential disappear in 3D, concluding that the occurrence of liquid-state anomalies in core-softened fluids strongly depends on the dimensionality of the system. (C) 2003 Elsevier B.V. All rights reserved.