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The purpose of this report is to develop a model of non-uniform beams within a software environment that lends itself to design, simulation, and analysis of dynamic systems. The beam is modeled by the Euler-Bernoulli approximation using the finite element method. Reformulation of the second-order symmetric beam equations into the fIrst-order state-space domain enables dynamic analysis and design from within the modern control paradigm. The MATLAB software package is chosen as it is the current state-of-the-art modeling environment for control engineering. This report will present the development of the modeling software, develop some of the underlying theory and limitations of the analysis, demonstrate its use in the dynamic modeling and analysis of an XM291 gun system, and validate its results against known analytic results.