TELPACK: an advanced TELetraffic analysis PACKage. A large class of teletraffic models can be analyzed through solving M/G/1, G/M/1, or QBD type Markov chains. A simple but non-restrictive rational structure assumption for such chains allows the use of invariant subspace computations in this analysis. Previous publications have discussed the various advantages of this approach. This paper introduces and discusses TELPACK, teletraffic analysis software that we have developed in C using CLAPACK routines. The software primarily relies on the matrix-sign function realization of the invariant subspace approach, and offers some traditional methods including the matrix-analytic ones as well. We also provide a brief review of the underlying theory with examples demonstrating the rational structure arising in some common teletraffic models