The problem of the normal reflection of a shock wave is solved by an approximate analytical integration of the hydrodynamical equations. The solution given here leads to nearly the same numerical results as an exact method, based on a graphical integration of the hydrodynamical equations, which has been described by Chandrasekhar. A method of computing the complete pressure-time curve at the reflector is given and applied to reflection in a class of fluids obeying the Tait adiabatic equation of state. It is found that in compressible fluids (gases) the pressure on the reflector is prolonged and that the impulse delivered to it exceeds the value predicted by the acoustic theory. In slightly compressible media (liquids and solids), on the other hand, the blow is shorter and the impulse delivered to the reflector is less than one would expect from the acoustic approximation. The method given here is also applicable to the reflection of gravity waves on the surface of a liquid.