Pulse-pileup in GBM occurs when several photons are detected in a single detector within a few microseconds of each other, causing the subsequent voltage signal to be distorted. This leads to inaccurate measurement of pulse heights, and hence distorts the recorded energy spectrum and complicates spectral modeling. The severity of this distortion increases as the input radiation intensity increases, becoming problematic for several source classes observed, including SGRs, TGFs, and solar flares. At a detection rate of 50,000 counts per second (per detector), about 5% of recorded energies are distorted. At a rate of 500,000 cps. about 55% of recorded energies are distorted. The measured count rate is also no longer approximated by a simple deadtime correction. By modeling event detection as a Poisson process, and using a model of the GBM hardware, we use probability theory to develop general expressions giving the recorded energy spectrum in terms of an input spectrum and intensity. We give a basic explanation of the model and examine some general cases of high-rate spectral distortions.