When rocks are cut in coal mines by steel picks, frictional heating sometimes causes ignition of methane; high speed water jets may provide a method of cutting which is free from this hazard. A high speed water jet emerging from a nozzle slows down with increasing distance from the nozzle and breaks up into water drops. Studies were made of the behaviour of water jets: in most of the experiments the jets were produced by pressures of 600 atm., but some results are given of experiments at pressures up to 5000 atm. The jets were examined by short exposure optical photography with several different methods of illumination (parallel transmitted, diffuse, and schlieren) and by X-ray photography. In order to find out how the jet velocity decays with distance from a nozzle, and to compare nozzle designs, a target plate containing a hole smaller than the jet diameter was placed so that the jet impinged at right angles on to it, and the target plate was moved until the maximum pressure at the hole was found: this was measured for different distances from the nozzle. Nozzle shapes suggested in literature for minimizing jet dispersion were studied and an empirical investigation of a variety of nozzle shapes was carried out. Several nozzle shapes were found which gave good results, i.e. the maximum pressure on the target plate was half the pump pressure at a distance of about 350 nozzle diameters. In many cutting applications the first stage in the process would be the impingement of a water jet on a surface at right angles. The initial cutting would depend upon the stress distribution within the target, which in turn would depend upon the pressure distribution produced by the water jet on the surface. A theory is given of the pressure distribution on the target plate, which predicts that the pressure will fall to zero at about 2$\cdot $6 jet radii: this was found to be in good agreement with experiments. Preliminary studies were made of the penetration of several types of rock by water jets of velocities up to about 1000 m/s (pressures about 5000 atm). It was found that a 1 mm diameter jet drills a cylindrical hole about 5 mm in diameter. The pressure that the water jet produces at the bottom of such holes was measured and shown to fall off to about one-tenth of the nozzle pressure at a hole depth of about 4 cm.