Accurate performance evaluation has always been an important issue in network design and analysis. Discrete event simulation has been known to be accurate but very time consuming. A particular performance metric of interest is the end-to-end blocking probability in a circuit-switched loss network. Various analytical approaches and approximation schemes have been suggested and among them, the fixed-point method, or reduced load method, has been receiving much attention. However, most of these schemes either consider only single traffic rate situations or multi-rate traffic under fixed routing. We develop an approximation scheme to estimate end-to-end blocking probability in a multi-rate multi-hop network with an adaptive routing scheme. The approximation results are compared with that of discrete event simulation. An example of application is also provided in which the proposed scheme is linked to the optimization tool CONSOL-OPTCAD to get network design trade-offs. This paper was presented at the "ATIRP ARL Federal Laboratory 2nd Annual Conference," February 5-6, 1998, University of Maryland, College Park campus.