The concept of mounting a loudspeaker on one end of a sound-absorbing tube has existed since at least 1936. Surprisingly, a detailed mathematical analysis of the configuration has not been performed, nor has a design method been established. This configuration, known as a transmission line loudspeaker, has received little consideration in the reviewed literature. Instead, it has become frequently featured in magazines for audio hobbyists, where it is experimentally designed with rules seemingly derived from hearsay and described with terms of high praise. In this dissertation, an electro-acoustical model of a fiberglass-filled transmission line is presented. This model represents the transmission line as two separate lines -- a mechanical line that models the mechanical motion of the fiberglass and an acoustical line that models the motion of the air. The lines are linked by the flow resistance of the fiberglass. From the model, solutions for the acoustic pressure, acoustical volume velocity of the air, mechanical velocity of the fiberglass fibers, and mechanical force on the fiberglass in the line are obtained. The fiberglass is characterized and empirical formulas that describe its characteristics are found. It is shown that the modeled input impedance to the transmission line is a good fit to measured data. The performance of the system is assessed by comparing it with the performances of typical loudspeaker mountings, i.e., the infinite baffle, the closed box, and the vented box. Finally, an example is shown of how the equations derived from the model can be used to evaluate the design of a transmission line loudspeaker system.