This thesis describes a Matlab implementation of the Implicitly Restarted Arnoldi Method for computing a few selected eigenvalues of large structured matrices. Shift-and-invert methods allow the calculation of the eigenvalues nearest any point in the complex plane, and polynomial acceleration techniques aid in computing eigenvalues of operators which are defined by m-files instead of Matlab matrices. These new Matlab functions will be incorporated into the upcoming version 5 of Matlab and will greatly extend Matlab's capability to deal with many real-world eigenvalue problems that were intractable in version 4. The thesis begins with a discussion of the Implicitly Restarted Arnoldi Method. The bulk of the thesis is a user's manual for the Matlab functions which implement this algorithm. The user's guide not only describes the functions' syntax and structure but also discusses some of the difficulties that were overcome during their development. The thesis concludes with several examples of the functions applied to realistic test problems which illustrate the versatility and power of this new tool.