A study has been carried out on the build-up of burn up wave in neutron absorbing and diffusive media. New parameters, i.e., transient length and transient time elapsing in establishing the steady burn up wave, have been introduced. The wave characteristics are expressed in terms of these new parameters and Full Width at Half Maxima (FWHM) and FullWidth at 1% of Maximum (FW1M). These characterization parameters would be useful in understanding the neutron burn up wave development and their approach to the equilibrium (steady) state.