This paper gives a general method to describe the motion of a spherically symmetric shock wave of varying strength moving in a gas where the density ahead of the shock front varies with distance from the centre. The method applies only as long as the density does not become zero ahead of the shock front at any instant. The motion is initiated by a central explosion which liberates a given amount of kinetic energy. The density distribution ahead of the shock front is shown to have an important effect on the variation in the shock strength, and a first approximation to the equation of motion of the shock front is deduced. A particular example is worked out in detail, and it is shown that for certain density distributions the blast wave consists of a thin shell of gas while the remainder of the original sphere is left intact.