The solution is obtained for the two-dimensional diffraction problem of a perfectly-reflecting strip subjected to a plane sharp-fronted pulse of constant unit pressure at normal incidence. Numerical calculations show in particular that the equalization of pressure round the strip 'overshoots' to produce pressures on the back of the strip up to a maximum of 21% in excess of the incident unit pressure, with pressures correspondingly below incident pressure on the front of the strip. The calculations also indicate that the pressure has become effectively steady, to within 3% or less, at the incident unit pressure in a time 5b/c after the pulse strikes the strip, where 2b is breadth of strip and c is velocity of sound. The extension to any shape of normally incident plane pulse is given in terms of our basic solution by simple application of the principle of superposition. The formal extension of the solution to the general case of any incident two-dimensional pulse field is also given. Finally, it is noted that the same general method can be applied to a number of related two-dimensional diffraction problems and in particular, solutions and numerical results have been thus obtained for the problems of a slit and a regular grating. It is proposed to consider these problems in further papers.