Abstract: It is described a process and an apparatus in which the cure of the concrete is accelerated by raising the temperature and moisture values in the environment in which the cure is taking place. The process comprises the following steps: making up at least a test piece obtained through the casting of a predetermined amount of concrete to be tested into a hollow mold; introducing the made up test piece into a vessel; adjusting the chemico-physical parameters of the environment in the vessel, following predetermined operating steps; operating a device adapted to measure the compression strength of the test piece, which brings about the generation of signals depending upon the measured compression strength; processing and displaying the signals.