A method is presented for studying hard-disk systems by Monte Carlo computer-simulation techniques within the NpT ensemble. The method is based on the Voronoi tesselation, which is dynamically maintained during the simulation. By an analysis of the Voronoi statistics, a quantity is identified that is extremely sensitive to structural changes in the system. This quantity, which is derived from the edge-length distribution function of the Voronoi polygons, displays a dramatic change at the solid-liquid transition. This is found to be more useful for locating the transition than either the defect density or the pressure-area isotherm.