This paper discusses the development of a semi-analytic one-dimensional model that can quickly calculate the reaction growth in shocked explosives for sustained pulses. A continuum approach has been adopted which seeks to approximate the complexity of hot spot growth by an implicit summation of these effects into a more readily calculable form. A "reactive wave" is identified that can be localized in such a manner as to contain all the necessary conditions for both the triggering and subsequent growth of reaction to detonation. An energy relationship is developed that is based on the initiation threshold curve. The relationship is constrained by the assumption that the wave contains minimum energy while operating at maximum efficiency in the rate of converting chemical energy into mechanical work within the explosive. As such, the method represents a possible limit to the efficiency of reaction growth in an explosive. A simple two-phase mixture model is employed to describe the partially reacted states within the explosive, and, in conjunction with the energy constraint, provides a unique boundary to the chemically active portion of the reactive wave. One (or at most two) adjustable coefficients are needed to provide an exact match with experiment. In general, the pattern of reaction growth is a good match to observed behaviour, and reaction rates are obtained from the model that are similar to those needed as input for one of the more widely used hydrocode-based methods((1)).