As of the development of this thesis, no commercially available products have been identified for the digital communication of instrumented data across a thick ({approx} 6 n.) steel wall using ultrasound. The specific goal of the current research is to investigate the application of methods for digital communication of instrumented data (i.e., temperature, voltage, etc.) across the wall of a steel pressure vessel. The acoustic transmission of data using ultrasonic transducers prevents the need to breach the wall of such a pressure vessel which could ultimately affect its safety or lifespan, or void the homogeneity of an experiment under test. Actual digital communication paradigms are introduced and implemented for the successful dissemination of data across such a wall utilizing solely an acoustic ultrasonic link. The first, dubbed the ''single-hop'' configuration, can communicate bursts of digital data one-way across the wall using the Differential Binary Phase-Shift Keying (DBPSK) modulation technique as fast as 500 bps. The second, dubbed the ''double-hop'' configuration, transmits a carrier into the vessel, modulates it, and retransmits it externally. Using a pulsed carrier with Pulse Amplitude Modulation (PAM), this technique can communicate digital data as fast as 500 bps. Using a CW carrier, Least Mean-Squared (LMS) adaptive …