The impingement region produced by directing a uniform, axisymmetric, supersonic jet of air normally onto a large, flat plate has been investigated experimentally and theoretically for four jets in the Mach number range 1·64 to 2·77. A qualitative theoretical description of the flow in the neighbourhood of the sonic line is given. A single-strip version of the method of Polynomial Approximation and Integral Relations (PIR) is applied to the flow, using two alternative methods of determining the centre-line shock height. The PIR predictions are compared to experimental shock shapes and pressure distributions. It is found that a PIR method in which the sonic line is assumed to intersect the shock at the jet edge leads to very good agreement with experiment at the higher jet Mach numbers, but accuracy is much reduced at the lower Mach numbers, the shock height being in error by about 62 per cent at a jet Mach number of 1·64. A change in flow pattern at small nozzle-to-plate distances is reported.