In this paper we propose using parametric modeling by employing a Multi-Pulse Excited Linear Predictive Coded (MPE-LPC) filter to synthesize the guitar. First we introduce different methods for sound synthesis. A detailed discussion including the derivation of LPC and MPE presented. Then we study the impulse and steady state response of the guitar signal. An implementation of the MPE-LPC method to model the guitar is covered in detail and opportunities to improve the compression ratio are discussed. We then present simulation results with a set of fixed parameters, which are used as a benchmark to observe performance trade-offs by varying the model parameters to improve the compression ratio. Finally, we discuss limitations of the modeling algorithm for use with wide-band transient musical sounds and possible applications of the MPE-LPC model as a method to dynamically calculate samples for use with wavetable synthesis of steady state sounds.